Chapter 3 Consumer Credit - Cengage · PDF fileChapter 3 Consumer Credit ... think of loans...

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Chapter 3

Consumer Credit

3-1 Introduction to Consumer Credit

3-2 Loans

3-3 Student Loans

3-4 Loan Calculations and Regression

3-5 Credit Cards

3-6 Credit Card Statement

3-7 Average Daily Balance

Live within your income, even if you have to borrow money to do so.—Josh Billings, American humorist

What do you think humorist Josh Billings meant in his quote?

Credit is a promise to pay in the future for goods and services you purchase today. When you think of consumer credit, you might think of loans and credit cards. Most people use credit. Using credit has advantages and disadvantages. Credit lets you enjoy purchases while you are paying for them. However, if you use credit irresponsibly, you may find yourself with debt that you cannot afford to pay. Being in debt is not a problem as long as you can make punctual payments to eliminate the debt.

Can you imagine your life without credit? If you had to save several years to buy a car, what would you use for transportation during the years you were saving? If you had to save for many years to purchase a home, where would you live while you were saving? Credit provides you with a way to increase your standard of living, as long as your purchases are made with careful financial planning.

What do you think?Traditionally, living within your income meant that if you needed to borrow money to buy something, you couldn't afford it. Living within your income does not mean not ever borrowing money. Nowadays, it means you should borrow what you can afford to repay. People who borrow are not automatically living beyond their means.

CHAPTER OVERVIEWDiscuss with students that credit is based on honesty, responsibility, and the ability to pay back the debt. Ask students if any of them have used their parents’ credit cards.

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147

Really?

Really!

The use of credit cards is incredibly prevalent in today’s society. Those little plastic cards are everywhere!

• There are more than 1.5 billion credit cards in use in the United States.

• The bank-issued credit card was created in the 1950s, and its creator, Frank McNamara, thought it would just be a fad!

• It is illegal for a company to send you a credit card you did not request. However, the typical American household receives about six credit card offers per month!

• All credit cards have length 85.60 mm and width 53.98 mm.

• There are more than 500,000 credit card transactions around the world—every minute!

• In 1983, MasterCard became the first credit card to use a hologram on its plastic cards, to help prevent counterfeiting.Clearly the small plastic card plays

a major role in how you conduct your financial life. A discussion about the credit card industry requires frequent use of numbers in the billions and trillions!

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REALLY? REALLY!Have students read the bullet points aloud. In the second bullet, the number one trillion is written out with all of its place-holding zeroes. This may be the first time students have ever seen it written this way. This is an opportune time to review million, billion, quadrillion, and so on. You can even suggest that students do Internet research to find the quantity googol, which is the number 1 followed by100 zeroes.

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148 Chapter 3 Consumer Credit

Objectives• Define basic credit terms.• Identify types of lending

institutions.• Compute finance charges for

installment purchases.

Key Termscreditdebtorcreditorassetearning powercredit ratingcredit reporting agencyFICO scoreinstallment plan

3-1 Introduction to Consumer Credit

down paymentdeferred payment planlayaway plandefault

What Do You Need to Know Before Using Credit?Goods and services can be purchased in one of two ways: “buy now, pay now” or “buy now, pay later.” If you purchase something that you do not pay for immediately, you are using credit. A person who uses credit is called a debtor. Every time you use electricity, you are using credit because you use the electricity and do not pay for it until the monthly bill arrives. A person who uses credit cards or takes out loans is also using credit. An organization or person that extends credit to a consumer is called a creditor.

There are advantages to using credit. You can shop without carrying large amounts of cash. You do not have to wait until you can pay in full to purchase something. Credit allows you to get use out of something while still paying for it. There are also disadvantages to using credit. Creditors charge interest on all purchases. Some people also feel that there is a tendency to overspend when using credit.

Any type of credit is based on honesty. Creditors need to be sure that they will be paid back before they extend credit. They will have you fill out an application for credit and will check your financial history. This history includes three basic items:

• Assets Everything you own—your home, car, bank accounts, and other personal possessions.

• Earning power Your ability to earn money now and in the future. Creditors want to make sure you have enough income to repay the debt.

• Credit rating Your credit “report card.” Every time you use credit, the creditor reports how well you met your financial obligations to a credit reporting agency.A credit reporting agency compiles records on all users of credit. These

records are used by creditors before they issue credit to a consumer. The best way

He that goes a borrowing goes a sorrowing.—Benjamin Franklin, American statesman

Warm-UpIf Sal saves $55 per month, express his total savings for x years as an expression in terms of x. 660x

EXAMINE THE QUESTIONCredit is not extended to young children because it requires a degree of financial and legal responsibility. Ask students what they think creditworthiness should be based on.

CLASS DISCUSSIONWhy does credit encourage overspending?

Has anyone ever encountered advertisements about obtaining your credit score on television, radio, or in print? For now, explain to students that their credit score is like a credit “report card.”

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3-1 Introduction to Consumer Credit 149

to start a good credit history is to open a savings and checking accounts, get a debit card, pay all your bills on time, and handle all your credit transactions successfully.

Consumers are given credit scores based on these three criteria. The most popular score is the FICO score, named for its creator, Fair, Isaac and Company. The scores, which range from 300 to about 850, summarize the probability that debtors will repay their debts. A higher score indicates a better credit rating. A person with a score near 800 is less of a risk to a creditor than a person with a score near 500. The FICO score is widely accepted by creditors as a reliable way to judge creditworthiness. Gender, race, religion, nationality, and marital status do not affect credit scores.

Any transaction involving credit is a legal contract obligating you to make timely payments. To use credit responsibly, you need to know the language of credit, and the laws that protect creditors and debtors.

Skills and Strategies

Some stores offer creditworthy customers the convenience of paying for merchandise or services over a period of time. This is an installment plan. The customer pays part of the selling price at the time of purchase. This is the down payment. The scheduled payments, or installments, are usually made on a monthly basis. Installment buyers are charged a fee. This fee is the interest and is added to the cost.

Whenever you purchase something on an installment plan, you are immediately paying interest on the purchase amount. When you buy on the installment plan, you immediately take possession of the item, agreeing to make payments of the purchase price plus interest over a period of time. Installment plans differ from deferred payment plans. A deferred payment plan also requires you to make periodic payments but there is no interest charged if these payments are made on time. With a deferred payment plan, you are paying the same price for the item as if you paid it in full at the time of purchase. With deferred payment plans, you take possession of the item immediately. Installment and deferred payment plans differ slightly from layaway plans. With a layaway plan, the customer does not receive the merchandise until it is paid for. It is held in the store for a fee. When all of the payments are made, you can take possession of the item. You learn about these plans in the next examples.

EXAMPLE 1

Heather wants to purchase an electric guitar. The price of the guitar with tax is $2,240. If she can save $90 per month, how long will it take her to save up for the guitar?

SOLUTION If Heather saves for the guitar, she is not using credit. But she will also not have use of the guitar while she is saving for it.

Divide 2,240 by 90. Round to the nearest tenth. 2,240 90 24.9<4

It will take Heather 25 months to save for the guitar. You can view Heather’s savings plan as an arithmetic sequence in which the first term is 90 and the common difference is 90. The 25th term is the earliest term greater than 2,240.

Check Your Understanding

If Heather’s guitar costs x dollars and she can save y dollars per month, express algebraically the number of months it would take Heather to save for the guitar.

TEACHStudents may already be familiar with the terms “down payment” and “interest.” When they think of interest, they think of receiving interest from a bank. The term “finance charge” indicates that the consumer is being charged interest, not receiving any interest.

EXAMPLE 1For problems involving how much to save, “normal” rounding rules are adjusted. If the answer is not an integer, always round up so that the amount saved is greater than the amount needed. Have students model this payment plan by identifying the first term and common difference of the related arithmetic sequence.

CHECK YOUR UNDERSTANDINGAnswer x

y

The answer must be rounded up if it is not an integer.

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EXAMPLE 3

Carpet King is trying to increase sales, and it has instituted a new promotion. All purchases can be paid on the installment plan with no interest, as long as the total is paid in full within 6 months. There is a $20 minimum monthly payment required. If the Schuster family buys carpeting for $2,134 and makes only the minimum payment for 5 months, how much will they have to pay in the 6th month?

SOLUTION This is a common business practice today. It is almost like a discount, except instead of saving money off the purchase price, the customer saves the finance charge.If the Schusters pay $20 for 5 months, they will have paid a total of $100. Subtract to find what they owe in the 6th month.

Purchase price – amount paid 2 52,134 100 2,034They will have to pay $2,034 in the 6th month. If this is not paid in full, there will be a finance charge imposed.

EXAMPLE 2

Heather (from Example 1) speaks to the salesperson at the music store, who suggests that she buy the guitar on an installment plan. It requires a 15% down payment. The remainder, plus a finance charge (interest), is paid back on a monthly basis for the next 2 years. The monthly payment is $88.75. What is the finance charge?SOLUTION Find the down payment by taking 15% of $2,240.Multiply $2,240 by 0.15. 0.15(2,240) 3365

Heather pays the store $336 at the time of purchase.She now has to make 2 years (24 months) of monthly payments of $88.75. The sum of the monthly payments is found by multiplying the number of payments by the monthly payment amount.Multiply $88.75 by 24. 24(88.75) 2,1305

The sum of the monthly payments is $2,130.Add down payment plus sum of payments. 336 2,130 2,4661 5

The total cost is $2,466.The finance charge is the extra money Heather paid for the use of credit. To find the finance charge, subtract the price of the guitar from the total cost. Total cost – purchase price 2 52,466 2,240 226Heather paid a finance charge of $226. That is the “fee” she paid for not having to wait two years to start using the guitar.


Assume the original price of the guitar was p dollars, and Heather made a 20% down payment for a 1-year installment purchase. The monthly payment was w dollars. Express the finance charge algebraically.

EXAMPLE 2The finance charge is also called the interest. In Chapter 2 the consumer earned interest, and now the consumer is paying interest.

EXAMPLE 3Tell students that the finance charge, imposed if the entire balance is not paid in full, usually has a relatively high interest rate. The finance charge applies retroactively to the day the loan was initiated.

CHECK YOUR UNDERSTANDINGAnswer (0.2p + 12w) – p, or 12w – 0.8p

Students should get comfortable with the simplest form of the expression, but they should recognize that the expression that is not in simplest form is also valuable because it models the sequence of events more clearly.

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EXAMPLE 4

Cecilia purchased $4,322 worth of home appliances on Appliance Depot’s deferred payment plan. The plan allows the customer to make no down payment, and there is no payment at all for 3 months. If the entire $4,322 is paid in full before the 3 months is up, there is no interest. (This is a store’s way to persuade customers to make purchases.) If it is not paid in full within the 3 months, there is a finance charge with an APR of 21.6% applied each month going back to the first month. If Cecilia makes the full payment a week after the 3 months expired, what is the finance charge?

SOLUTION

Divide to find the monthly interest rate.

21.6% 12 1.8%4 5 , or 0.018

Find the interest after the first month by multiplying.

4,322 0.018 77.803 5 , rounded to the nearest cent.

Find the balance after the first month by adding the interest to the balance.

4,322 77.80 4,399.801 5

The balance for the second month is $4,399.80 before computing the second month’s interest.Find the second month’s interest by multiplying.

4,399.80 0.018 79.203 5 , rounded to the nearest cent.

Add to find the second month’s balance including interest.

4,399.80 79.20 4,4791 5

The third month’s balance is $4,479 before interest is computed.

Multiply and add to get the third month’s balance including the interest. 4,479 0.018 80.623 5 , rounded to the nearest cent.

4,479 80.62 4,559.621 5 .

The amount due the week after the 3-month offer expired is $4,559.62.Subtract to find how much interest Cecilia incurred by being a week late.

4,559.62 4,322 237.622 5

Cecilia cost herself $237.62 by being only a week late, which is a great deal of money. Imagine if this was a 1-year deferred payment plan, and it was paid late!


The Whittendale family purchases a new refrigerator on a no-interest-for-one-year plan. The cost is $1,385. There is no down payment. If they make a monthly payment of x dollars until the last month, express their last month’s payment algebraically.


If Cecilia’s plan was a 2-year deferred payment plan and she paid it a week late after the 2 years, would her total interest be more or less than $1,800? Explain.

CHECK YOUR UNDERSTANDINGAnswer $1,385 – 11x

Point out that x could be a minimum monthly payment, and x would not necessarily be

equal to 1,38512

.

EXAMPLE 4Point out to students that there could also be a late fee, as well as interest charged on the extra week it took Cecilia to pay. They could compute this by prorating the 7-day week based on what would have been the fourth month’s interest. Students should clearly see that not complying with the interest fee conditions can be very expensive.

CHECK YOUR UNDERSTANDINGAnswer More; the monthly

compounded interest on $4,322 at 21.6% for 2 years is greater than $2,000.

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EXAMPLE 5

Circuit Town is having a huge sale on large screen TVs. Anita purchased a 60-inch curved-screen TV for $2,045.15 including sales tax. This purchase was made on a 6-month layaway plan. She had to pay a monthly payment of $361. What is the sum of the monthly payments? What was the fee charged for the layaway plan?

SOLUTION Determine the total of Anita’s monthly payments.$361 6 $2,1663 5

Anita’s total cost for the TV is $2,166 on the layaway plan. Since the TV sold for $2,045.15, subtract that amount from the total of her monthly payments.

2,166 2,045.15 120.852 5

The layaway fee for this purchase is $120.85. Keep in mind, Anita was able to lock in the sale price by using the layaway plan even though she didn’t have the full amount at the time of purchase, but she does not have use of the item immediately.


Marty is making a layaway purchase of a $1,500 couch at Frank’s Furniture Store. He will be paying $156 every 2 weeks for 20 weeks on a layaway plan. What is the layaway fee for this purchase?

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EXAMPLE 5Point out to students that a person who buys on a layaway plan does not take possession of the merchandise until it is paid in full. In that respect, it is not “really” using credit.

CHECK YOUR UNDERSTANDINGAnswer $60

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Credit ScoresYour credit score affects the interest rate a creditor charges you, and borrowers with lower scores pay higher interest rates. This is because they are a greater credit risk to the lender. Lenders are always concerned about a borrower who may default on a loan. A debtor defaults when they fail to make payments according to the schedule set up when the loan originated. Credit scores change as new data about a person’s credit becomes available. FICO scores higher than 700 signify a good credit rating and those above 770 are considered excellent.

Generally, any person with a credit score below 600 is considered a significant risk to the creditor. Individuals with scores at 700 or greater qualify for the best interest rates available.

EXAMPLE 6

Mike has a credit rating of 720. Tyler has a credit rating of 560. Mike and Tyler apply for identical loans from Park Bank. Mike is approved for a loan at 3.2% interest, and Tyler is approved for a loan that charged 3 percentage points higher because of his inferior credit rating. What interest rate is Tyler charged?

SOLUTION Add 3% to3.2%.3% 3.2% 6.2%1 5

Tyler will pay 6.2% interest for the same loan.While the arithmetic in this problem may have been simple, the message is important: Credit scores will affect the interest you pay on loans. If you are a good credit risk, you will save money when you borrow money.Tyler’s loan will have cost him more than Mike’s loan for the same amount over the same period of time. The extra dollar amount of what Tyler pays could be hundreds of dollars or even more, depending on the original loan amount.


Janet had a credit score of 660. She then missed three monthly payments on her credit cards, and her score was lowered x points. Express her new credit score algebraically.

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EXAMPLE 6Make students aware that their credit rating not only affects whether or not they get a loan, it affects the interest rate they pay.

CHECK YOUR UNDERSTANDINGAnswer 660 – x

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Applications

1. Interpret the quote in the context of what you learned about consumer credit in this section.

Solve each problem. Round monetary amounts to the nearest cent.2. Monique buys a $4,700 air conditioning system using an installment plan that

requires 15% down. How much is the down payment? 3. Craig wants to purchase a boat that costs $1,420. He signs an installment

agreement requiring a 20% down payment. He currently has $250 saved. Does he have enough for the down payment?

4. Jean bought a $1,980 snow thrower on an installment plan. The installment agreement included a 10% down payment and 18 monthly payments of $116 each.

a. How much is the down payment? b. What is the total amount of the monthly payments? c. How much did Jean pay for the snow thrower on the installment plan? d. What is the total finance charge? e. If Jean models her payment plan as an arithmetic sequence, give the first

term a1 and the common ratio d.5. Linda bought a washer and dryer from Millpage Laundry Supplies for y

dollars. She signed an installment agreement requiring a 15% down payment and monthly payments of x dollars for 1 year.

a. Express her down payment algebraically. b. How many monthly payments must Linda make? c. Express the total amount of the monthly payments algebraically. d. If Linda models her payment plan as an arithmetic sequence, give the first

term 1a and the common ratio d. e. Express the total amount Linda pays for the washer and dryer on the

installment plan algebraically. f. Express the finance charge algebraically.

6. Zeke bought a $2,300 bobsled on an installment plan. He made a $450 down payment, and he has to make monthly payments of $93.50 for the next 2 years. How much total interest will he pay?

7. Gary is buying a $1,250 computer on an installment plan. He makes a down payment of $150. He has to make monthly payments of $48.25 for 2 1

2 years. What is the total finance charge?

8. Mazzeo’s Appliance Store requires a down payment of 13 on all installment

purchases. Norton’s Depot requires a 30% down payment on installment purchases. Which store’s down payment rate is lower?

9. Ari purchased a microwave oven on an installment plan for m dollars. He made a 20% down payment and agreed to pay x dollars per month for two years. Express the finance charge (interest) algebraically.

He that goes a borrowing goes a sorrowing.—Benjamin Franklin, American statesman

See margin.

$705

No

$198$2,088

$2,286$306

a1 = 198; d = 116

0.15y12

12x

a1 2 0.15y; d = x

12x = 0.15y(12x + 0.15y) 2 y, or 12x 2 0.85y

$394

$347.50

Norton’s

0.2m + 24x 2 m, or 24x 2 0.8m

TEACH Algebraic RepresentationsStudents having difficulty with algebraic representations should be encouraged to mimic the previous numeric examples.

Options to BuyDescribe the difference between rent-to-own and layaway plans. In rent-to-own plans, the consumers have the use of the product before paying in full. In layaway, they do not get the product until payment is made in full.

Finance ChargesAs each finance charge problem is completed, ask students if they feel that the interest is a worthwhile fee for having the use of the product sooner than if money were saved before making the purchase.

ANSWERS1. Borrowing money is a

tremendous responsibility; it ties up future income, and sometimes borrowers regret borrowing. Borrowers also pay a fee (interest) for borrowing.

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10. Adam bought a $1,670 custom video game/sound system on a special no-interest plan. He made a $100 down payment and agreed to pay the entire purchase off in 1½ years. The minimum monthly payment is $10. If he makes the minimum monthly payment up until the last payment, what will be the amount of his last payment?

11. Max created a spreadsheet for installment purchase calculations.

A B C D E F G H

1Purchase

Price

Down Payment Percentage as a

Decimal Down

PaymentMonthly Payment

Time in Years

Time in Months

Total of Monthly

Payments

Finance Charge

(Interest)

2 $1,200 0.20 f. $97.01 1 j. n. s.

3 $1,750 0.10 g. $71.12 2 k. p. t.

4 $1,340 0.15 h. $77.23 1.5 l. q. u.

5 $980 0.10 i. $165.51 0.5 m. r. v.

a. Write a spreadsheet formula to compute the down payment in cell C2. b. Write a spreadsheet formula to compute the time in months in cell F2. c. Write a spreadsheet formula to compute the total of monthly payments in

cell G2. d. Write the spreadsheet formula to compute the finance charge in cell H2.

e. Use your answers to a–d to fill in the missing entries f–v.12. If Tanya purchased a $1,700 set of golf clubs on a 9-month layaway plan

and had to pay a monthly payment of $201, what is the sum of the monthly payments? What was the fee charged for the layaway plan?

13. Chris purchases living room furniture for $4,345 from Halloran Gallery. She has a 1-year, no-interest, no-money-down, deferred payment plan. She does have to make a $15 monthly payment for the first 11 months.

a. What is the sum of these monthly payments? b. How much must Chris pay in the last month of this plan? c. What is the difference between the layaway plan in Exercise 12 and the

deferred payment plan in Exercise 13?14. Audrey purchases a riding lawnmower using a 2-year, no-interest deferred

payment plan at Lawn Depot for x dollars. There was a down payment of d dollars and a monthly payment of m dollars. Express the amount of the last payment algebraically.

15. Some stores offer a rent-to-own plan. The customer makes a down payment, receives the merchandise at time of purchase, and makes monthly payments. The sum of the monthly payments is lower than the cost of the item. When the last payment is made, customers make a choice. They can purchase the item and apply their payments toward the cost. They can return the item, which means they rented it for a certain period of months.

a. Sharon bought a $2,100 high-definition television (HDTV) on a 6-month rent-to-own plan. The down payment was 10%. What was the dollar value of the down payment?

b. Her monthly payments were $75 per month. If she decides not to buy the HDTV after the 6 months, what was her cost to rent it?

16. Bernie bought a refrigerator at a special sale. The refrigerator regularly sold for $986. No down payment was required. Bernie has to pay $69 per month for 1½ years. What is the average amount Bernie pays in interest each month?

$1,400

= A2*B2= 12*E2

= D2*F2

= C2 + G2 − A2

See margin.

$1,809; $109

$165$4,180

See margin.

x − d − 23m

$210

$660

$14.22

ANSWERS11e.f. $240g. $175h. $201i. $98j. 12k. 24l. 18m. 6n. $1,164.12p. $1,706.88q. $1,390.14r. $993.06s. $204.12t. $131.88u. $251.14v. $111.06

13c. With the layaway plan, you do not receive the merchandise until payment is made in full. With the deferred payment plan, you receive the merchandise immediately.

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17. Lillian purchased a violin from Smash Music Stores. It regularly sold for $670, but was on sale at 10% off. She also had to pay 8% sales tax. She bought it on an installment plan and paid 15% of the total cost with tax as a down payment. Her monthly payments were $58 per month for 1 year.

a. What is the discount? b. What is the sale price? c. What is the sales tax? d. What is the total cost of the violin? e. What is the down payment? f. What is the total of the monthly payments? g. What is the total she paid for the violin on the installment plan? h. What is the finance charge? i. If Lillian models her payment plan as an arithmetic sequence, give the first

term a1 and the common ratio d.18. The following inequalities give information on your credit scores. Let x

represent your credit score.• If 700.x , your credit score is excellent.• If x, ,680 700, your credit score is good.• If x, ,620 680, your credit score should be watched carefully.• If x, ,580 620, your credit score is low• If 580,x , your credit score is poor.

If Mary Ann’s credit score is low, but she receives 40 points for paying off some delinquent debts, is it possible that her credit rating is now good? Explain.

19. Samantha’s grandfather is debt-free—he bought his car and his house without taking out a loan. He saved and paid cash. He wanted to take out a loan to buy Samantha a car for college graduation. The bank turned him down. Explain why.

20. The following arithmetic sequence models an installment purchase. Give the down payment, monthly payment, and length of the plan. 400, 510, 620, 730, 840, 950, 1,060.

$67$603

$48.24$651.24

$97.69$696

$793.69$142.45

First term = 97.69; common difference = 58

See margin.

See margin.

Down payment = $400; Monthly payment = $110; length of plan 6 months

ANSWERS18. No. Even if her low credit

rating was 620, it would only increase to 660, which is not in the “good” range.

19. He had no credit history and had a low credit score as a result. He had no proof he could make timely payments over a period of time.

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3-2 Loans 157

What Information Do You Need to Know Before Taking Out a Loan?Whenever you borrow money, you must sign an agreement, called a promissory note, which states the conditions of the loan. Your signature is your promise to pay back the loan as outlined in the agreement. Always read an entire promissory note carefully before signing it.

The loan amount you borrow is the principal. The interest rate you pay is given per year and is the annual percentage rate (APR). The promissory note contains information that the creditor is required to state, as stipulated in the Truth in Lending Act. This includes the principal, APR, monthly payment, number of payments that must be made, interest due dates for each payment, and fees for late payments.

Not all loan agreements are the same, so each promissory note describes the features of that particular loan. Become familiar with the terms below.

• Cosigner This person agrees to pay back the loan if the borrower is unable to do so. People without an established credit rating often need a cosigner.

• Life insurance A creditor often requires a borrower to have life insurance that will cover the loan in the event the borrower dies before the loan is paid.

• Prepayment privilege This feature allows the borrower to make payments before the due date to reduce the amount of interest.

• Prepayment penalty This agreement requires borrowers to pay a fee if they wish to pay back an entire loan before the due date.

Objectives • Read monthly payments from a

table.• Compute monthly payments

using a formula.• Compute interest on loans.

Key Termspromissory noteprincipalannual percentage ratecosignerlife insuranceprepayment privilegeprepayment penaltywage assignmentwage garnishmentballoon payment

3-2 Loans

Warm-UpEvaluate each expression when x 35 .a. x x(1 )1

b. x

x

11

1

c. xx

Lend money to an enemy, and thou will gain him; to a friend, and thou will lose him.—Benjamin Franklin, American statesman and inventor

lending institutioncollateralpayday loan

27

64

2.370370...

EXAMINE THE QUESTIONTaking out a loan requires you to sign a legal document called a promissory note. It will include many paragraphs of fine print, all of which must all be read carefully.

Before taking out a loan, you need to know the different types of lending institutions and understand legal terms used in the promissory note.

CLASS DISCUSSIONFinance charge is another name for interest.

It is not a benefit to the bank for loans to be paid off early, since that reduces the amount of interest collected.

Which types of lending institutions have you heard of? Are there any locally?

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• Wage assignment This is a voluntary deduction from an employee’s paycheck, used to pay off debts. If a debtor’s employer and the creditor agree, loans can be paid off using this form of electronic transfer.

• Wage garnishment This is an involuntary form of wage assignment, often enforced by court order. The employer deducts money from the employee’s paycheck to pay the creditor.

• Balloon payment The last monthly payment on some loans can be much higher than the previous payments. These high payments are called balloon payments.An organization that extends loans is called a lending institution. Lending

institutions are businesses that make profit by charging interest. There are many types of lending institutions, including:

• Banks are institutions where most consumers apply for loans. Savings banks offer good interest rates but require loan applicants to have good credit ratings. Commercial banks are banks used by businesses, so they have large amounts of money to lend. They also require a good credit rating.

• Credit unions provide financial services for members only. Members may work in the same office, be in the same profession, or live in the same area. Members deposit money in a credit union account. This money is made available to members who apply for loans from the credit union, usually at a lower interest rate than a bank can offer. The rate is lower because credit unions, unlike banks, do not operate to make a profit and, as a result, are exempt from certain federal and state taxes.

• Consumer finance companies are businesses that primarily lend money to people with poor credit ratings who cannot get a loan anywhere else. High interest rates are charged for this service.

• Life insurance companies make loans to their policyholders only. The amount that can be borrowed is based on the amount of life insurance purchased and the length of time the policy has been held. The interest rate is good because the life insurance company is not taking a tremendous risk because if the loan is not paid back, it can be deducted from the life insurance benefit when it is paid.

• Pawnshops are known for small, quick loans. A customer who needs money leaves a personal belonging, called collateral, with the pawn broker in exchange for the loan. Most loans are 30-, 60-, or 90-day loans. When the debtor returns with the principal plus interest, the collateral is returned.

• Payday loan stores offer a payday loan, a small loan taken over a very short period of time, usually a few weeks or less. The borrower agrees to pay back the loan in full on their next payday. The APR is huge for these types of loans, but they are available to borrowers with poor credit ratings. Proof of employment is required for all borrowers.You may have seen loan sharks in the movies. Loan sharks charge extremely

high interest rates and do not formally check your credit rating. Loan sharking is illegal.

Regardless of where you shop for a loan, the Equal Credit Opportunity Act requires a creditor to treat you fairly. If your application is turned down, you are protected by the Fair Credit Reporting Act, which says that the lender must give you the reason in writing for the loan denial. Always compare the terms of the loan and the annual percentage rates when shopping for a loan.

CLASS DISCUSSIONHighlight the differences between the types of lending institutions.

How would you decide which type of institution from which to borrow?

While banks are the most popular student response, the popularity of some cable TV pawnshop shows have exposed more students to how pawnshops work.

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3-2 Loans 159


Monthly loan payments are computed using a formula. Payment information is often arranged in tables to make it easy for customers.

EXAMPLE 1

What is the monthly payment for a $4,000 2-year loan with an APR of 4%?

SOLUTION The table lists monthly costs per $1,000 borrowed. Divide the amount you want to borrow by 1,000. Look across the row labeled 4% and down the column labeled 2-Year Loan. The monthly cost per thousand dollars borrowed is $43.42. You are borrowing four sets of $1,000, so the table amount must be multiplied by 4.

43.42 4 173.683 5

The monthly payment is $173.68.

Monthly Payment per $1,000 of Loan

Interest Rate (APR) 2-Year Loan 3-Year Loan 4-Year Loan 5-Year Loan

1% $42.10 $28.21 $21.26 $17.09

2% $42.54 $28.64 $21.70 $17.53

3% $42.98 $29.08 $22.13 $17.97

4% $43.42 $29.52 $22.58 $18.42

5% $43.87 $29.97 $23.03 $18.87

6% $44.32 $30.42 $23.49 $19.33

7% $44.77 $30.88 $23.95 $19.80


Juan is borrowing $41,000 for 5 years at an APR of 3%. Using the table above, find the monthly payment.

EXAMPLE 2

What is the total amount of the monthly payments for a $4,000, 2-year loan with an APR of 4% according to the table in Example 1?

SOLUTION There are 12 months in a year, so the borrower will make 24 monthly payments in 2 years. Use the monthly payment from Example 1, $173.68. Multiply the monthly payment by 24.

173.68 24 4,168.323 5

The total of the 24 monthly payments is $4,168.32.

Extend Your Understanding

The total of the monthly payments for a 5-year loan is $10,692. The APR is 7%. How much money was originally borrowed?


What is the total amount of the monthly payments for a $5,300, 4-year loan with an APR of 3%?

TEACHThe formula to compute monthly payments requires careful placement of parentheses. Calculator entry must be done carefully. Students need to use their “financial number sense” to check each problem when they are finished.

EXAMPLE 2You can review the number of months in 1, 1.25, 1.5, and 1.75 years. Students should become familiar with yearly equivalents of 15 months, 18 months, 30 months, and so on.

EXAMPLE 1The table is abbreviated; it only offers selected interest rates and numbers of years. Explain the need for an algebraic formula to handle any loan conditions.

CHECK YOUR UNDERSTANDINGAnswer 736.77

Some students may forget that the table amounts are per $1,000 of principal.

CHECK YOUR UNDERSTANDING22.13*5.3 = 117.29 * 48 = $5,629.92

EXTEND YOUR UNDERSTANDINGAnswer $9,000

Students can use trial and error after they get the monthly payment per $1,000 in the 5-year column.

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EXAMPLE 3

Find the finance charge for a $4,000, 2-year loan with a 4% APR.

SOLUTION Use the total amount of the monthly payments from Example 2 and subtract the borrowed amount.

4,168.32 4,000 168.322 5

The finance charge for this loan is $168.32.


Karl is borrowing x dollars over a 3-year period. The monthly payment is y dollars. Express his finance charge algebraically.

EXAMPLE 4

Mark bought a new car. The total amount he needs to borrow is $28,716. He plans on taking out a 4-year loan at an APR of 3.12%. What is the monthly payment?

SOLUTION Mark must use the monthly payment formula, since 3.12% is not in the table.Monthly Payment Formula

121

12

112

1

12

12MP r r

r

t

t5

1

1 2

MPrt

====

where monthly paymentprincipalinterest ratenumber of years

Substitute P 5 28,716, r 5 0.0312, and t 5 4.

28,716 0.0312

121 0.0312

12

1 0.031212

1

12(4)

12(4)M 5

1

1 2

Simplify the exponent to make calculator entry easier.

28,716 0.031212

1 0.031212

1 0.031212

1

48

48M 5

1

1 2

Use your calculator. Enter in one keystroke sequence, but work slowly and carefully. Round to the nearest cent.

(28716(0.0312/12)(1+0.0312/12)^48)/((1+0.0312/12)^48-1)

The monthly payment is $637.13.


Find the monthly payment for a $1,000, 1-year loan at an APR of 2.5%.

EXAMPLE 3Remind students that thefinance charge is the sameas the interest.

CHECK YOUR UNDERSTANDINGAnswer 36y − x

EXAMPLE 4Ask students what purpose the fraction bar serves besides indicating division. Guide students to understand that the fraction bar also serves as a grouping symbol. When the formula is entered into the calculator, they must think about the order of operations and if parentheses are needed for proper calculator entry.

After the discussion, you can have students insert the parentheses when they write the formula in their notes.

Also remind students that their answers must make sense, and often, if the numerical entries are put into the calculator incorrectly, an unreasonable answer is displayed.

CHECK YOUR UNDERSTANDINGAnswer $84.47 (using the formula)

Sometimes the table and the calculator will differ, due to rounding, and the bank will adjust the last payment to make sure the finance charge is correct after the last payment is made.

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3-2 Loans 161

EXAMPLE 5

Natasha needs to borrow $400 until her next paycheck to purchase a wedding gift. She goes to Friendly Fred’s Loan Store. Friendly Fred lends her the $400 for 3 weeks, at which time Natasha pays it back in full. There is no collateral required, so the APR is relatively high. Fred charges her $70 interest for the 3 weeks. What is the APR for this loan to the nearest 10%?

SOLUTION Natasha needs to compute the payday loan APR using the following formula.

Payday APR Loan interestLoan amount

Loan length in days5 4 3

365

100

Substitute. 70400

21365

1005 4 3APR

Solve. 5302%.APR


Harrison’s Loan Stars loaned Nicole $900 that she needed for an unexpected car repair. She must repay the loan in 30 days. The interest is $100. What is the APR for this loan, to the nearest percent?

© A

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a Lu

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/ww

w.S

hutte

rsto

ck.c

om

EXAMPLE 5Some students may enter the entire computation on one set of keystrokes, while others may first express each fraction as a decimal and then round each fraction. Students doing the entire problem with one keystroke sequence would get 304%. Either method rounds to 300%.

CHECK YOUR UNDERSTANDINGAnswer 135%

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Applications

1. Interpret the quote in the context of what you learned about loans in this section and on your experiences or expectations.

2. Arrange the following lending institutions in descending order according to their APRs for a $10,000, 2-year loan.

East Meadow Savings 4 12

%

Clinton Park Credit Union 4%

Tivoli Trust 4 38

%

First Bank of Rhinecliff 4.45%

Columbia Consumer Finance Corp. 4 916

%

3. How many more monthly payments are made for a 5-year loan than for a 2-year loan?

4. How many monthly payments must be made for a 2½-year loan?5. Bart needs to borrow $7,000 from a local bank. He uses the table of monthly

payments on page 159 to compare the monthly payments for a 3% loan for three different periods of time.

a. What is the monthly payment for a 2-year loan? b. What is the monthly payment for a 3-year loan? c. What is the monthly payment for a 5-year loan?

6. Darnelle has a $10,000, 3-year loan with an APR of 5%. She uses the table on page 159 to compute information on the loan.

a. What is her monthly payment? b. What is the total of all her monthly payments? c. What is the finance charge?

7. Melissa wants to check the accuracy of the finance charge on her promissory note. She has a $6,000, 4-year loan at an APR of 3.11%. Round to the nearest cent.

a. What is her monthly payment? b. What is the total of all her monthly payments? c. What is the finance charge?

8. The policy of the Broadway Pawnshop is to lend up to 35% of the value of a borrower’s collateral. John wants to use a $3,000 ring and a $1,200 necklace as collateral for a loan. What is the maximum amount that he could borrow from Broadway?

9. Jordan is taking out a 2-week payday loan for $600. He will be charged $95 interest for the 2-week loan. What is the APR for this loan?

10. Juliana is taking out an $8,700, 3-year loan with an APR of 2.31%. What will be the monthly payment for this loan? Round to the nearest cent.

Lend money to an enemy, and thou will gain him, to a friend, and thou will lose him.—Benjamin Franklin, American statesman and inventor

TEACHFor exercises involving monthly payments, students should be provided with the formula for these exercises.

On tests, you can give them an option—to take a test with or without the formula sheet. You can offer bonus points for students who elect to memorize the formulas.

Exercise 4This exercise requires students to use the number of months as a fraction of a year. Extra practice can be given at the board.

Exercise 5This is a typical analysis most borrowers do so they can choose the term of a loan. The advantage to a long period is a low monthly payment. The disadvantage is more total interest.

Exercise 7Point out to the students that, equipped with their monthly payment formula, they can check to ensure the bank is doing the calculations on their loans correctly.

ANSWERS1. Borrowing money from a

friend can create problems. Friends can take advantage of one another since repayment is not structured with a legal contract.

See margin.

Columbia, East Meadow, First Bank, Tivoli, Clinton Park

36

30

$300.86$203.56$125.79

$299.70$10,789.20

$789.20

Round to the nearest cent. $133.10$6,388.80

$388.80

$1,470

413%

$250.37

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3-2 Loans 163

11. Lavonda took out a $7,500 loan with an APR of 3.875% and agreed to pay it back monthly over 6 years. How many monthly payments did she make?

12. Solomon is taking out a $15,320, 2-year loan with an APR of 3.29%. What will be the finance charge for this loan to the nearest dollar?

13. Reggie needs a quick x-dollar loan until his next payday in 2 weeks to take advantage of a sale on ski equipment. The bank would take too long on the paperwork, so he goes to a pawnshop. The pawnshop will only lend him 25% of the value of his collateral. Express algebraically the amount of collateral Reggie must use for this loan.

14. Olivia is considering membership to the Regional Teachers’ Credit Union so that she can save money on a loan. The credit union will lend her $8,000 for 3 years at 2.25% APR. The same loan at her savings bank has an APR of 2.9%. How much would Olivia save in finance charges if she joined the credit union and took out her loan there? Round to the nearest ten dollars.

15. Rob wants to purchase a $5,000 drum set. The music store offers him a 2-year installment agreement requiring $800 down and monthly payments of $202.50. Rob has a poor credit rating.

a. What is his interest on this installment agreement? b. Instead of using the store’s installment plan, Rob can borrow $5,000 at an

APR of 7% from a local consumer finance company. What would be the monthly payment for this loan using the table from Example 1? Round to the nearest cent.

c. How much interest would the finance company charge? d. Should Rob use the installment plan or borrow the money from the finance

company?16. Lee wanted to compute the monthly payment on a 2-year, $8,400 loan at an

APR of 3.07%. She entered the keystrokes at the right on her calculator. The display gives an answer of 48, which Lee knows is incorrect. Explain what her error was.

8400(0.0307/12)(1+0.0307/12)^24/(1+0.0307/12)^24-1

17. A loan used for buying a home is called a mortgage. The Fortunato family is borrowing $430,000 to buy a home. They are taking out a 30-year mortgage at a rate of 3.55%.

a. Compute the monthly payment to the nearest cent. b. Find the total of all of the monthly payments for 30 years. c. What is the total interest? d. Which is greater, the interest or the original cost of the home?

18. The following spreadsheet can be used to compute monthly payments given the APR, principal, and term of the loan.

A B C D E

1Principal in

DollarsInterest Rate as a Decimal Time in Years

Time in Months

Monthly Payment

2 11,000 0.03 4 c. f.

3 900 0.027 0.5 d. g.

4 2,500 0.034 2 e. h.

a. Write the spreadsheet formula to compute cell D2. b. Write the spreadsheet formula to compute cell E2. c–h. Use your spreadsheet to fill in the missing entries.

72

$531

4x

$80

$660

$223.85$372.40

Finance company.

See margin.

$1,942.91$699,447.60

$269,447.60Home

=12*C2See margin.See margin.

TEACHExercise 16 This exercise demonstrates the need to use parentheses carefully, and why students need to use number sense when reviewing their answers.

ANSWERS16. The parentheses that group

the entire numerator and the parentheses that group the entire denominator were omitted.

17. The mortgage amount is $430,000, after any down payment.

18b. =(A2*(B2/12) (1+B2/12)^D2)/ ((1+B2/12)^D2−1)

c. 48d. 6e. 24f. $243.48g. $151.18h. $107.90

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How Can You Pay for a Post–High School Education?Every high school student has aspirations. You may not know now exactly what you want to do or be in the future, but it is safe to say that you want more than to just be a high school student. Once you graduate, there are options to be explored as a student of higher education, an employee at a job, or a member of the military.

This section focuses on the education option and the essential question of how you will pay to attend a school of higher education. Examine these statistics on student loans.

• More than 60% of higher-education students borrow to cover the costs.• There is more than $1.2 trillion in student loan debt and that amount is

expected to increase.• Student loan debt is the second highest household debt (mortgage debt is the

highest).• The class of 2015 graduated with an average student loan debt of $35,051.• Annual costs at institutions of higher learning are projected to reach $102,000

for private institutions and $45,500 for public institutions by 2033. • It is reported that more than $20 billion in profit is generated each year from

the debts students incur.

Objectives• Explain the options available for

student loans.• Calculate the interest due in various

student loan situations.• Apply the simplified daily interest

formula.

Key Termscareer school Free Application for Federal Student

Aid (FAFSA)

Student Aid Report (SAR)

expected family contribution (EFC)

federal loanprivate loanFederal Direct Subsidized

Loan (Stafford)deferFederal Direct Unsubsidized

Loan (Stafford)accruesFederal PLUS LoanFederal Perkins Loan

3-3 Student Loans

Warm-UpEvaluate the expressions

rn

nt1

1 11 2

and rn

nt1

11

1

2

when r 0.15 , n 125 ,

and t 25 . Round to nearest hundredth.

Debt certainly isn’t always a bad thing. A mortgage can help you afford a home. Student loans can be a necessity in getting a good job. Both are investments worth making, and both come with fairly low interest rates.—Jean Chatzky, financial journalist

interest capitalizationsimplified daily interest formula

4.54−0.18

EXAMINE THE QUESTIONBefore discussing how to pay for a post–high school education, ask students what they think a post–high school education is. Their responses should include 2- and 4-year colleges and universities, community colleges, technical colleges, career training schools, military schools, and more. Ask them what they think attendance at those institutions might cost. Invariably, the discussion will come around to taking out a loan. The details of student loans are covered in this section.

CLASS DISCUSSIONThe bulleted points in the opening paragraphs offer students some eye-opening data on the student loan industry. After reviewing these facts, ask students what they already know about student loans and how they came across that information.

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3-3 Student Loans 165

Higher education is more than just colleges and universities. Another option is career schools, which are specialized institutions that provide students with the necessary skills to be successful at a particular job. Career schools are sometimes known as trade, vocational, or technical schools. Take a look at this brief list of career school programs. These are only a few of the many opportunities available.

Appliance RepairAutomotive RepairCarpentryCosmetologyCulinary ArtsElectronicsGraphic Design

Health CareHospitalityInformation TechLandscapingMedical AssistantNursingPhotography

Physical TherapyReal EstateVeterinary TechnicianWeldingX-Ray Technician

Students wishing to attend career schools can apply for subsidized and unsubsidized federal loans just as students who want to attend colleges and universities. It is important to note that the school you choose must be accredited and participate in the federal aid program.

Whether higher education in your future comes in the form of attending a 4-year college or university, a community college, or a career school, chances are that you will need to take out a loan. For most students, securing a loan to pay for higher education costs is a necessity. Like many major purchases, you need to “do your homework” before signing on the dotted line for any student loan. The first thing that you and/or your family needs to do is to complete the Free Application for Federal Student Aid, informally known as FAFSA. It can be accessed at fafsa.ed.gov. Each applicant must supply personal and financial data that will assist in the loan decision-making process. Although it is a federal form, many private educational and lending institutions require it as well. Once the form is completed and processed, you will receive a Student Aid Report, or SAR. This report will indicate the expected family contribution, or EFC, along with other important information about loans that may be available to you.

There are two major types of student loans that you can apply for: federal loans and private loans. The federal government funds and makes available a federal loan. A loan issued by a bank, a credit union, a school, or even a state agency is considered a private loan. Your financial situation may dictate which type of loan you are eligible for. There are some substantial differences between the two that include pay-off terms, interest rates, and more.

There are a number of different federal loans available, as listed below. You can obtain detailed information from the Office of the U.S. Department of Education about these types of federal loans at www.studentaid.ed.gov. Most loans have a limit to the amount that can be borrowed depending on a number of factors. The federal government sets the interest rates from year to year.

• Federal Direct Subsidized Loan (Stafford Loan) These are need based. Students are able to defer interest payments for a period of time. That is, no payment is required on the loan while the student is in school and during a 6-month grace period after graduating. The U.S. Department of Education pays the interest while you are attending school and during the 6-month grace period.

• Federal Direct Unsubsidized Loan (Stafford Loan) These are not need based and you are expected to pay the interest that accrues (builds up) from the time you receive the money. No payments are required while you are attending school and during the 6-month grace period after graduation.

TEACH If you have Internet access in the classroom, display the sites recommended here. Show students what is available to them online to assist in the student loan process.

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• Federal PLUS Loan (Parent Loan for Undergraduate Students) These loans allow parents (or graduate students) to borrow money for college costs. The borrowers must be creditworthy.

• Federal Perkins Loan This type of loan is available for students with exceptional financial need.It is extremely important to examine all forms of financial aid that are

available to you. If you are interested in a career school, there are a variety of options beyond the traditional federal and private loans that you should explore. The Federal Student Aid website (www.studentaid.ed.gov) is a great source for all types of information on what might be available to you. In addition to doing the research, more importantly, you need to “do the math.” In the examples that follow, you learn how and when interest on a student loan accrues. For private and federally unsubsidized loans, the interest will accrue from the moment the money is credited to the student’s account. For federally subsidized loans, the interest does not accrue while the student is in school and during the 6-month grace period after graduation. Whatever loan you choose to apply for, be sure you understand all of the repayment options and how they can affect the total amount you will pay over the life of the loan.


The examples that follow will assist you in making financial decisions about loan payment options.

EXAMPLE 1

As an incoming college freshman, Ariana received a 10-year, $9,100 Federal Direct Unsubsidized Loan with an interest rate of 4.29%. She knows that she can begin making loan payments 6 months after graduation but interest will accrue from the moment the funds are credited to her account. How much interest will accrue while she is still in school and over the 6-month grace period for this freshman-year loan?

SOLUTION With an unsubsidized loan, students are responsible for interest accrued while they are in school and during the grace period. While they don’t have to start loan payments until 6 months after they leave school, the interest starts to accrue as soon as funds are credited.The student loan interest during the nonpayment period is calculated using the simple interest formula I Prt5 . P 5 9,100, r 5 0.0429, t 5 4.5 (4 years plus 6-month grace period)

9,100 0.0429 4.5I 5 p p

$1,756.765IHer new principal at the end of 4.5 years is the sum of the loan amount, $9,100, and the interest, $1,756.76.


Write the formula for the amount of interest that would accrue over 4 years in college plus a 6-month grace period on a Y-year loan in the amount of A dollars at an interest rate of R.

TEACHThere are five types of student loans listed (four federal and one private). Divide the class into five groups. Assign each group a type of loan and have them do research to find informational websites. Make a list of the websites and what they have to offer.

EXAMPLE 1The federal loan interest rate used in this chapter was in effect at the time of the writing of this section. It may have changed. Research to find what the new rate is and inform students about the increase or decrease. All of the examples and exercises in this section use the federal loan interest rate of 4.29%.

CHECK YOUR UNDERTSANDING

Answer 4.5AR100

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Interest CapitalizationAriana has a choice. She can wait until the end of the grace period and have all of the interest accrued added to the principal. Then she would start repaying her loan using the new principal, which is the sum of the loan amount and the interest accrued during the nonpayment period. In this case, she pays nothing for the 4 years in school and the 6-month grace period. During that time, interest still accrues at 4.29%. Her accumulated interest will be added to the loan when the repayment period begins. This is known as interest capitalization. The interest will increase the loan principal and she will then be paying interest on both the original loan amount and the interest accrued for the first 4.5 years.

Her second option is that she could pay only the interest each month while in school and during the grace period so that at the end of 4.5 years, her loan amount for freshman year is still $9,100. The next few examples help you see how mathematics can assist in making the decision about which interest option is best for your circumstances.

EXAMPLE 2

Ariana can elect to defer all payments during the 4.5-year period. Her loan balance would then be the sum of the amount borrowed and the interest accrued over the 4.5-year nonpayment period. Determine the interest she would pay on this loan.

SOLUTION The new principal P is the sum of the loan amount and the interest accrued during the nonpayment period found in Example 1.

9,100 1,756.765 1P10,856.765P

Use the monthly payment formula.

121

12

112

1

12

12MP r r

r

t

t5

1

1 2

Let P 510,856.76, r 5 0.0429, t 5 10.

10,856.76 0.0429

121 0.0429

12

1 0.042912

1

120

120M 5

1

1 2

Her monthly payments would be approximately $111.42. Her total payments ($111.42 × 120) would be $13,370.40. Her interest for the loan is $13,370.40 – 9,100, or $4,270.40. This brings the total payment for the loan to $13,370.40.


Luke took out a 10-year Federal Direct Unsubsidized loan for $15,000 with a 4.29% APR. If he makes no payments during the first 4.5 years, what will the new loan amount be?


Suppose Ariana had taken out a subsidized loan for the same amount at the same interest rate for the same loan length. How much interest would she have to pay for the time she is in school and during the 6-month grace period?

TEACHMake sure that students understand the financial ramifications of interest capitalization. Basically, if interest payment is deferred, a student will wind up paying interest on the interest that was owed (but allowed to be deferred). The examples that follow show students how the mathematics of paying the interest during the deferment period leads to paying less for the loan in the long run.

EXAMPLE 2This example shows students the monetary effect of interest capitalization. Ask them to point out where the “interest on the interest” is being calculated.

CHECK YOUR UNDERTSANDINGAnswer $17,895.75

EXTEND YOUR UNDERSTANDINGAnswer $0; it is subsidized, so the federal government covers that part of the interest.

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EXAMPLE 3

Suppose that Ariana only paid the interest during her 4 years in school and the 6-month grace period. What will Ariana now pay in interest over the term of her loan?

SOLUTION Ariana has already paid $1,756.76 in interest over the 4.5-year period. At the end of the 4.5 years, Ariana now has a 10-year loan at 4.29% on the original loan amount of $9,100.00.Use the monthly payment formula.

121

12

112

1

12

12MP r r

r

t

t5

1

1 2

Let P 59,100, r 5 0.0429, t 5 10.

9,100 0.042912

1 0.042912

1 0.042912

1

120

120M 5

1

1 2

93.39<M

Ariana’s monthly payment would be approximately $93.39.Her total payment is the product of her monthly payment and the number of months she will be making those payments.

Total Payment $93.39 120 $11,206.805 3 5

The loan interest is the difference between the total payment and the loan amount.

Interest $11,206.80 $9,100$2,106.80

5 2

5

Ariana will pay $2,106.80 in interest over the 10-year period for borrowing $9,100. Her total interest is the sum of the interest from the nonpayment period and the interest accrued over the 10-year loan life.

Total Interest 1,756.76 2,106.80$3,863.56

5 1

5

This brings the total payment for the loan to $12,963.56.


What percent of the original loan amount of $9,100 would Ariana be paying in interest if she only paid the interest during the 4.5-year period preceding the start of the loan repayments?

EXAMPLE 3Make sure students understand the difference between Examples 2 and 3. Have them compare the results from both. What conclusions can be made from the calculations?

CHECK YOUR UNDERSTANDINGAnswer 42.5%

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James has a $7,500 unsubsidized 10-year loan with an interest rate of 4.29%. He wants to pay only the interest while he is attending school. His payment is due on the 10th of each month. He made his last payment on February 10, and this year is a leap year. Calculate the amount that he will pay on March 10. (Keep in mind that there are 366 days in a leap year.)

Examples 2–4 illustrate different payment options with an unsubsidized loan. Perkins loans and subsidized Stafford loans work differently than unsubsidized loans because interest does not accrue until the student begins repayment. Private student loans are similar to car and personal loans. As soon as the money is deposited into the student account, the borrower is expected to make payments. It is critical that you understand all of the payment options for whatever loan you get.

EXAMPLE 4

In Example 3, Ariana chose to pay only her interest each month. It is due on the first of the month. How did Ariana calculate the interest she needed to pay?

SOLUTION Ariana used the simplified daily interest formula, which gives her the amount of interest accrued since the last time she made a payment. Basically, the formula determines the daily interest amount for the year using the simple interest formula and then multiplies that amount by the number of days, d, since the last payment.

interest rate expressed as a decimalInterest Since Last Payment (I) Principal number of dayssince last payment365

5 3 3

3655I Pd

r

Suppose Ariana made an interest payment on March 1. Her next interest payment is due on April 1, which is 31 days from the last payment.Let P 5 9,100, d 5 31, and r 5 0.0429

5 3 3I 9,100 31 0.0429365

I 33.16<Ariana should make a payment of $33.16 for March.Note that Ariana can also use the simplified daily interest formula to calculate a daily interest amount by using d 3655 , or 366 in a leap year. Notice then how the simplified daily interest formula becomes the simple interest formula you learned in Section 2-3.

365(365)

3655 5 5I Pd

rI P

rI Pr→ →

This is the simple interest formula: 5I Prt , where 15t year.This will yield the interest for one year. She then can get the daily interest amount by dividing the yearly interest by 365 (or 366 in a leap year). Once she has the daily interest amount, she can multiply that by the number of days since she last made a payment. In order to make sure that she covers the full amount, the daily rate should be rounded up to the nearest penny.

EXAMPLE 4The simplified daily interest formula can be viewed in two ways, depending on where the denominator is placed. In the formula given,

365r

takes the annual interest rate expressed as a decimal and divides it by 365 to find the daily interest rate expressed as a decimal. Had the 365 been

the denominator under d 365

d

rather than under r, the fraction

365d represents the fractional

part of a year that covers the time from the last payment. Both ways of presenting the formula are acceptable and understandable.

CHECK YOUR UNDERSTANDINGAnswer $25.49

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Pete took out a private, 8-year loan for $6,000 at an interest rate of 5.56%. How much will he pay in interest?

As you can see from these examples, there is plenty of math to be done before making a decision about which loan to choose. In many instances you might wind up taking a combination of loans. The paperwork you keep will be very important so that you can pay all of the loans on time and avoid getting any penalty charges.

EXAMPLE 5

Instead of a federal loan, suppose that Ariana had been able to get a private loan at a slightly higher interest rate of 6.4% for the same period of time with immediate repayment. That is, as soon as the funds are deposited in her account, she must begin making the monthly payments. What would her monthly payment be? What would her total payment be? How much would she have paid in interest?

SOLUTION Use the monthly payment formula.

121

12

112

1

12

12MP r r

r

t

t5

1

1 2

Let P 5 9,100, r 5 0.064, t 5 10.

9,100 0.06412

1 0.06412

1 0.06412

1

120

120M 5

1

1 2

102.87<MAriana’s monthly payment would be approximately $102.87.Her total payment is the product of her monthly payment and the number of months she will be making those payments.

Total Payment $102.87 120$12,344.40

5 3

5Her interest for the loan is the difference between the total payment and the loan amount.

Interest $12,344.40 $9,100$3,244.40

5 2

5

Ariana will pay $3,244.40 in interest over the 10-year period for borrowing $9,100 and begin making monthly payments when the principal is deposited in her account.

EXAMPLE 5The private student loan rate listed in this problem was one of the many rates in effect at the time of this writing. Research current rates and let students know what the rate is now. Unlike the federal rate, the private loan rates fluctuate based on a variety of factors.

CHECK YOUR UNDERSTANDINGAnswer $77.57

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1. Read the quote at the beginning of this section. Interpret the quote in terms of what you have learned about student loans.

Use the following situation to answer questions 2–6.Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this nonpayment time, interest will accrue at 4.29%.

2. How much interest will Rich accrue during the 4.5-year nonpayment period?

3. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.

a. What will the new principal be when he begins making loan payments? b. How much interest will he pay over the life of the loan?

4. Suppose Rich only paid the interest during his 4 years in school and the 6-month grace period. What will he now pay in interest over the term of his loan?

5. Rich made his last monthly interest-only payment on November 1. His next payment is due on December 1. What will be the amount of that interest-only payment?

6. Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year loan with an interest rate of 5.9%.

a. Determine his monthly payment. b. What is the total amount he will pay back? c. What is the total interest amount?

7. Martina’s grandparents paid for the first 3 years of her college costs. As a senior, she was approved for a federal unsubsidized loan in the amount of $9,300 at a 4.29% interest rate for 10 years.

a. If she chooses to make interest-only payments until the monthly loan payments are due, for how long will she be making interest-only payments?

b. What would be the total amount of her interest-only payments? c. If she begins her loan repayment with no interest capitalization since she

already paid the interest when she was in school and during the 6-month grace period, how much will she have paid in interest for this loan by the end of the 10-year loan period?

8. Ted is a freshman attending a 4-year college. He has been approved for an $8,000 subsidized federal loan at 4.29% for 10 years. How much will the U.S. Department of Education subsidize in interest costs during his 4.5-year nonpayment period?

Use the following situation to answer questions 9–13.

Applications

Debt certainly isn’t always a bad thing. A mortgage can help you afford a home. Student loans can be a necessity in getting a good job. Both are investments worth making, and both come with fairly low interest rates.—Jean Chatzky, Financial journalist

TEACHThere are a variety of scenarios in the problems offered here. It is important that students classify problems by the types of loans and by whether or not interest is being capitalized. You might want to review a few of the problems ahead of time with students to make sure they understand the categories into which the problems fall.

ANSWERS1. Chatzky tries to ease our fears

about carrying responsible debt. There are some major expenses in life that can’t be paid for without taking out a loan. She believes that if the investment is worth making, then the debt is worth carrying.

$1,525.10

$9,425.10$3,707.60

$3,354.70

$27.86

$87.31$10,477.20

$2,577.20

1.5 years$598.46

$2,752.46

See margin.

$1,544.40

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Britta has been accepted into a 2-year medical assistant program at a career school. She has been awarded a $6,000 unsubsidized 10-year federal loan at 4.29%. She knows she has the option of beginning repayment of the loan in 2.5 years. She also knows that during this nonpayment time, interest will accrue at 4.29%.

9. How much interest will Britta accrue during the 2.5-year nonpayment period?10. If Britta decides to make no payments during the 2.5 years, the interest will be

capitalized at the end of that period. What will the new principal be when she begins making loan payments?

11. Suppose Britta only paid the interest during her 2 years in school and the 6-month grace period. What will she pay in interest over the term of her loan?

12. Britta made her last monthly interest-only payment on May 5. Her next payment is due on June 5. What will be the amount of that interest-only payment?

13. Suppose that Britta decided to take out a private loan for $6,000 for which loan payments start as soon as the loan amount is deposited in her account and continue for 10 years. The interest rate is 6.1%.

a. Determine her monthly payment. b. What is the total amount she will pay back? c. What is the total interest amount?

14. There are many online student loan calculators that can assist you. Examine the input boxes for one such calculator (Cost of Interest Capitalization Calculator www.finaid.org). After clicking “calculate,” the following information is reported:Comment 1: After the deferment period of 54 months, the new loan balance is $6,561.78, including $1,061.78 in accrued interest.Comment 2: Without the interest capitalization there would have been 120 payments of $56.45 adding up to $6,774.00 (including a total of $1,274.00 in interest) plus an additional $1,061.78 in interest paid during the deferment period.Comment 3: With the interest capitalization, there are 120 payments of $67.34 for a total payment of $8,080.80 (including a total of $1,519.03 in interest plus $1,061.78 in interest accrued during the deferment period).Comment 4: The total amount paid with interest capitalization is $8,080.80, or $245.03 more than would have been paid without capitalization. That’s an extra $0.04 for every dollar borrowed.Answer the questions below based on the comments above.

a. Examine comment 1. Explain the way in which a student chose to make payments if this comment applies.

b. Examine comment 2. Explain the way in which a student chose to make payments if this comment applies.

c. Examine comment 3. Explain the way in which a student chose to make payments if this comment applies.

d. Comment 4 states that the difference between “with interest capitalization” and “without interest capitalization” results in an extra $0.04 for every dollar borrowed. Explain how that was calculated using the data given in this comment.

Loan Balance 5500

Interest Rate 4.29

Deferment in Months 54

Capitalization At Repayment

Loan Term in Years 10

$643.50

$6,643.50

$2,033.10

$21.86

$66.91$8,029.20

See margin.

$2,029.20

14a. No payments were made for 4.5 years. The interest was capitalized.

14b. Interest was paid during the 4.5 years. Loan repayment began after 4.5 years and continued for 10 years. The total interest for this loan is the sum of the interest paid during the nonpayment period and the interest accrued during the 10-year loan life.

14c. The student deferred all payments for 4.5 years. The accrued interest was added to the loan amount. The monthly payment is higher than without the capitalization.

14d. The difference between the interest amounts is $243.03. $6,000 was borrowed. Divide 243.03 by 6,000. The result is $0.04 interest per dollar borrowed.

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3-4 Loan Calculations and Regression 173

How Can You Calculate and Model Loan Computations?Before taking out a loan, you need a complete picture of what your payment responsibilities will be over the life of the loan. Part of the monthly payment decreases your principal and part is the finance charge or interest.

In a savings account, the interest is an amount of money that you get from the bank as compensation for keeping your money there. For loans, interest is the amount of money that you have to give to the bank as a fee for using their money.

There are many monthly payment calculators available on the Internet that can give you a summary of the loan balance over the lifetime of the loan and on a monthly or yearly basis.

Examine the summary statement at the right of a loan calculator for a $100,000 loan with an APR of 5.5% for a period of 5 years, taken out in January 2017. Notice the interest you must pay is close to 15% of the amount that was borrowed.

You can get a better idea of how your monthly payment is allocated by looking at a payment schedule for the first year of the loan. Notice, as the months pass, the principal that is paid off by your monthly payment of $1,910.12 increases as the interest amount decreases. Pick any month. The sum of the principal paid and the interest paid will always be approximately

Jan. 2017

Feb. 2017

Mar. 2017

Apr. 2017

May 2017

Jun. 2017

Jul. 2017

Aug. 2017

Sept. 2017

Oct. 2017

Nov. 2017

Dec. 2017

$100,000

MONTHLY PAYMENT $ 1,910.12

PAYMENTS and INTEREST

TOTAL INTEREST PAID (LIFE OF LOAN) $ 14,606.97

LOAN AMOUNT

DATE

$1,451.78

5.50%

$1,458.44

$1,465.12

$1,471.84

$1,478.58

$1,485.36

$1,492.17

$1,499.01

$1,505.88

$1,512.78

$1,519.71

$1,526.68

PRINCIPAL

INTEREST RATE

5 Years

$458.33

$451.68

$444.99

$438.28

$431.53

$424.76

$417.95

$411.11

$404.24

$397.34

$390.40

$383.44

INTEREST

TERM

Jan-17

$98,548.22

$97,089.78

$95,624.66

$94,152.82

$92,674.24

$91,188.88

$89,696.71

$88,197.71

$86,691.83

$85.179.05

$83,659.34

$82,132.66

BALANCE

START DATE

Objectives • Determine the interest on a loan

given the principal, time, and APR.• Use the logarithmic loan length

formula to determine the term of a loan.

• Use regression to find the curve of best fit using data from a loan table.

Key Termsmonthly payment calculatorloan length formula cubic functioncubic regression equation

3-4 Loan Calculations and Regression

Warm-UpDetermine if the given point is on the graph of 2x – 3y 5 12.

a. (6, 4)b. (–6, –8)c. (0, 4)

Loans and debts make worries and frets.

—Traditional Proverb

EXAMINE THE QUESTIONStudents will model monthly loan payment figures using the loan formula and regression analysis.

CLASS DISCUSSIONDiscuss how a loan balance works. Although the monthly payment remains the same, the contributions to principal and finance charge do not.

noyes

no

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equal to your monthly payment due to rounding. Look at how much of your payment goes to paying off the interest on the loan. Before taking out any loan, it is important to carefully examine a loan schedule as shown here so you can get a better idea of where you will stand financially at any given time during the borrowing period.


Here you learn how to use formulas and regression analysis to make loan calculations in order to make wise credit decisions.

EXAMPLE 1

Determine the total interest owed on a 5-year, $10,000 loan at 6% APR.

SOLUTION

Use the monthly payment formula. 121

12

112

1

12

12MP r r

r

t

t5

1

1 2

Substitute P 5 10,000, r 5 0.06, and t 5 5. 10,000 0.06

121 0.06

12

1 0.0612

1

12(5)

12(5)M 5

1

1 2

Use your calculator. Enter in one keystroke sequence. Consider order of operations to determine where parentheses are needed.

193.32805M

The monthly payment is approximately $193.33.Multiply the monthly payment by the number of monthly payments to find the total of the monthly payments.

193.33 60 11,599.803 5

The total of the monthly payments is $11,599.80.Keep in mind that this is not the exact amount. The amount of the monthly payment was rounded to the nearest cent, or two decimal places, but in reality, banks keep decimal amounts when performing calculations.To find the interest you must pay, subtract the loan principal from the total payback.

11,599.80 10,000 1,599.802 5

The interest on a $10,000 loan at 6% APR taken out for 5 years is approximately $1,599.80.


Hannah is taking out a 4.3% loan to purchase an $18,000 car. The length of the loan is 8 years. How much will she pay in interest?

TEACHBefore focusing on the loan table ask students what the total interest charge might be on a $100,000 15-year loan with an APR of 5.5%. How far off were their interest estimations from the actual amount?

EXAMPLE 1Before students use their calculator, discuss the careful use of parentheses. Be sure they understand that the fraction bar makes parentheses unnecessary in the book, but the calculator is different. Have them try a monthly payment formula on the calculator with and without the parentheses in the denominator.

CHECK YOUR UNDERSTANDINGAnswer $3,305.28 It is necessary to calculate the monthly payment using the formula ($221.93) and then determine the total amount that will be paid back by multiplying the monthly payment by 96 ($21,305.28). Subtracting the loan amount from the total yields $3,305.28 extra that was paid toward interest.

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The Loan Length FormulaRecall the work you did with logarithms in Sections 2-9 and 2-10. Since a logarithm is an exponent, we once again use logarithms to solve for time in the monthly payment formula introduced in Section 3-2. By solving for t in that formula, we arrive at the loan length formula. The development of the loan length formula is beyond the scope of this course. It employs both algebraic manipulations and the properties of logarithms to solve for time t. Here, we introduce the loan length formula in two forms: one using common logarithms and the other using natural logarithms. In both cases, t represents the loan length in years, M represents the monthly payment, P represents the principal, and r represents the interest rate expressed as a decimal.

Loan Length Formula (with common logs)

5

2 2

1

log log12

12log 112

t

MP

MP

r

r

Loan Length Formula (with natural logs)

5

2 2

1

ln ln12

12ln 112

t

MP

MP

r

r

Both formulas yield the same result. As a matter of fact, a log with any base would work as well, but the natural and common logs are used above since calculations with them do not require the change-of-base formula. These formulas are used in the next example.

EXAMPLE 2

Claude wants to borrow $25,000 to purchase a car. After looking at his monthly budget, he realizes that all he can afford to pay per month is $300. The bank is offering a 5.9% loan. What would the length of his loan need to be so that he could stay within his budget?

SOLUTION To solve this problem, we can use either version of the loan length formula. Here we will use the loan length formula with common logs.

Substitute P 5 25,000, M 5 300, and r 5 0.059. t 5

2 2

1

log 30025,000

log 30025,000

0.05912

12log 1 0.05912

Calculate to the nearest

hundredth of a year. 8.96<tClaude would need to take out a loan for about 9 years.


In Example 2, what impact would an increase in the monthly payment of $50 have on the length of the loan?


Use the information for Example 2 and the loan length formula using natural logarithms to show that you get the same result for t, approximately 9 years.

EXAMPLE 2As stated, either version of the loan length formula can be used to solve the problem. If students are inputting the formula in their calculator as one fraction, it is important that the numerator and the denominator both be enclosed in a set of parentheses. Before doing the calculations, offer students the following numerical example: 10 6

22 .

Clearly, it is equal to 2. But using the calculator sequence 10 – 6/2 will yield a different answer than (10 – 6)/2. Show students the numerical example:10 62 * 2

2 . The correct answer should is 1.

When using a calculator, this can only be attained by putting parentheses around the entire denominator. (10 – 6)/2*2 yields 4 as an answer whereas (10 – 6)/(2*2) yields the correct answer of 1. Show them how the same holds in the loan length formulas.

TEACHMake sure students understand that borrowers can’t usually tailor the loan length to meet their needs. The loan lengths give you an idea of the minimum length of time a loan can be taken out to achieve the affordable monthly payment.

TEACHSince the variable representing time in the monthly payment formula is an exponent, solving for that exponent requires the use of logarithms. Briefly review the concept of logarithms. Remind students that a logarithm is an exponent. Introduce the two loan length formulas on this page. Ask students to point out similarities and differences. The structure of both formulas is the same but one uses a common logarithm and the other uses a natural logarithm. Both are acceptable in this situation. These formulas are complex. Make sure that students understand that the proper placement of the parentheses as shown here is essential to correct calculations.

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EXAMPLE 3

John does not have a very good credit rating. In January of 2016, he found a lending institution that was willing to loan him $100,000 for 15 years at a higher than normal interest rate of 7.5% because of his poor credit rating. Examine the table of decreasing loan balances over the 15-year period. Use regression to determine a curve of best fit for this data.SOLUTION Use the statistics features on your graphing calculator to make a scatter plot of the ordered pairs (x, y) where x equals the year number and y equals the loan balance.To simplify the data-entry process, rather than using the actual years, let year 2016 be year 1, 2017 be year 2, and so on.Use the linear regression analysis covered in Section 1-5 to determine the linear regression equation, 6,777.54 110,001.045 2 1y x , with numbers rounded to the nearest hundredth. Notice that the line doesn’t follow the shape of the points.To get a more accurate regression equation, use quadratic regression. Rather than determining a linear equation, you determine a quadratic regression equation. A quadratic equation has the form 25 1 1y ax bx c. A quadratic equation has the shape of a parabola. While the scatter plot may not look completely parabolic, the points might best fit on part of a parabola.The quadratic regression equation is

251.10 2,760.02 98,618.0625 2 2 1y x x , with numbers rounded to the nearest hundredth.For even more accuracy, you can use cubic regression. A cubic equation has the form

3 25 1 1 1y ax bx cx d. This function is known as a cubic function since the highest exponent in the equation is a 3. The cubic regression equation is 6.23 101.67 3,747.49 100,142.233 25 2 2 2 1y x x x , with numbers rounded to the nearest hundredth.It appears that this regression equation approaches the shape of the points better than the quadratic or the linear equations. While the cubic above may not yield the exact equation to determine loan balances through the life of the loan, it does yield fairly accurate amounts.

Year End-of-Year Loan Balance

2016 $96,248.64

2017 $92,206.05

2018 $87,849.63

2019 $83,155.00

2020 $78,095.92

2021 $72,644.09

2022 $66,769.01

2023 $60,437.85

2024 $53,615.17

2025 $46,262.84

2026 $38,339.72

2027 $29,801.51

2028 $20,600.46

2029 $10,685.11

2030 $0.00


Use the linear, quadratic, and cubic regression equations determined in Example 3 to compare the computed loan balances when x 25 with the loan balance amount given in the chart for 2017.

CHECK YOUR UNDERSTANDINGAnswer The length of the loan would drop to about 7.35 years if the monthly payment is increased by $50.

EXTEND YOUR UNDERSTANDINGStudents will see that both forms of the loan length formula will yield the same results.

EXAMPLE 3Answer The purpose of this problem is to introduce students to other forms of regression equations. It walks them through linear, quadratic, and cubic regression. The point is not that the payment formula is a cubic regression. Rather, Example 3 shows that the cubic regression yields a better approximation of the values stated in the table.

CHECK YOUR UNDERSTANDINGAnswer linear: $96,445.96; quadratic: $92,093.62; cubic: $92,190.73; chart: $92,206.05

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1. How might the quote apply to what you have learned in this section?2. What is the total interest on a 10-year, 6.1% loan with a principal of $32,000?3. Jamie wants to borrow $15,000 from South Western Bank. They offered her a

4-year loan with an APR of 5.5%. How much will she pay in interest over the life of the loan?

4. Charlie and Kathy want to borrow $20,000 to make some home improvements. Their bank will lend them the money for 10 years at an interest rate of 5.75%. How much will they pay in interest?

5. Devon is considering taking out a $7,000 loan. He went to two banks. Stevenson Trust Company offered him an 8-year loan with an interest rate of 8.6%. First National Bank offered him a 5-year loan with an interest rate of 10%. Which loan will have the lower interest over its lifetime?

6. A bank offers a $25,000 loan at an interest rate of 7.7% that can be paid back over 2–10 years.

a. Write the monthly payment formula for this loan situation. Let t represent the number of years from 2 to 10 inclusive.

b. Write the total interest formula for this loan situation. Let t represent the number of years from 2 to 10 inclusive.

c. Construct a graph. Let the independent variable represent years and the dependent variable represent the interest paid.

d. Use your graph to estimate the interest for a 6½-year loan.7. Jennifer wants to borrow $20,000. Her bank offers a 7.1% interest rate. She can

afford $500 a month for loan payments. What should be the length of her loan to the nearest tenth of a year?

8. Louis wants to take out a $14,000 loan with a 6.8% APR. He can afford to pay no more than $400 per month for loan payments. What would be the length of his loan? Round to the nearest tenth of a year.

9. Use your answer and the loan information from Exercise 8 to determine what effect a $50 decrease in Louis’s monthly payment would have on the length of his loan.

10. Dave wants to borrow $22,000 from First Finance Bank. The bank will give him a 15-year loan at an interest rate of 4.85%. How much will he pay the bank in interest over the life of the loan? Round to the nearest hundred dollars.

Loans and debts make worries and frets.—Traditional Proverb

Applications

TEACHExercises 2–5 Here students are asked to determine the total interest over the life of the loan. They will need to first determine the monthly payment and then multiply that monthly payment by the loan length in months. Subtracting the principal from that amount will yield the desired result.

$10,824.40

$1,744.80

$6,344.80

See additional answers.

See additional answers.

See additional answers.approx. $6,800

3.8 years

3.3 years

The loan length would increase to 3.8 years.

$9,000

Exercise 6Students may need some assistance in setting up an appropriate viewing window when graphing. Keep in mind that the formula calculates a monthly payment, but the independent variable for the graph is stated in years.

ANSWERS1. The proverb is a warning

about loans and debts. Entering into any debt agreement should be made cautiously.

5. First National: Stevenson, $2,705.60; First National, $1,923.80

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11. Use the given yearly payment schedule.

a. What is the loan amount? b. What is the length of the loan? c. What is the monthly

payment? d. What is the total interest paid? e. Construct a scatter plot using

the data points (year, loan balance).

f. Write a linear regression equation that approximates the year–loan balance relationship. Round to the nearest hundredth.

g. Write a quadratic regression equation that approximates the year–loan balance relationship. Round to the nearest hundredth.

h. Write a cubic regression equation that approximates the year–loan balance relationship. Round to the nearest hundredth.

12. Use the given payment schedule. a. What is the loan amount? b. What is the length of the

loan? c. What is the approximate

monthly payment rounded to the nearest cent?

d. What is the total interest paid over the life of the loan?

e. Construct a scatter plot using the data points (year, loan balance).

f. Write a linear regression equation that approximates the year–loan balance relationship. Round to the nearest hundredth.

g. Write a quadratic regression equation that approximates the year–loan balance relationship. Round to the nearest hundredth.

h. Write a cubic regression equation that approximates the year–loan balance relationship. Round to the nearest hundredth.

1. 2. Year Principal Paid Interest Paid Loan Balance

$35,000.00

2010 $773.32 $3,291.90 $34,226.68

2011 $850.08 $3,215.15 $33,376.60

2012 $934.44 $3,130.78 $32,442.16

2013 $1,027.18 $3,038.04 $31,414.97

2014 $1,129.13 $2,936.10 $30,285.84

2015 $1,241.19 $29,044.65

2016 $1,364.38 $27,680.27

2017 $1,499.79 $26,180.48

2018 $1,648.64 $24,531.84

2019 $1,812.26 $22,719.57

$2,700.85

$2,565.44

$2,416.59

$2,252.96

$2,824.03

Yearly Payment Schedule

2020 $1,992.13 $2,073.10 $20,727.45

2021 $2,189.84 $1,875.39 $18,537.61

2022 $2,407.18 $1,658.05 $16,130.43

2023 $2,646.08 $13,484.34

2024 $2,908.70 $10,575.64

2025 $3,197.38 $7,378.26

2026 $3,514.72 $3,863.54

2027 $3,863.54 $0.00

$1,156.53

$867.84

$550.51

$201.69

$1,419.14

Year Principal Paid Interest Paid Loan Balance

$10,000.00

1 $680.52 $775.41 $9,319.48

2 $737.01 $718.92 $8,582.47

3 $798.18 $657.75 $7,784.29

4 $864.43 $591.50 $6,919.86

5 $936.17 $519.76 $5,983.69

6 $1,013.88 $4,969.81

7 $1,098.03 $3,871.78

8 $1,189.16 $2,682.62

9 $1,287.86 $1,394.76

10 $1,394.76 $0.00

$357.90

$266.77

$168.07

$61.18

$442.05

$10,00010 years

$1,455.93$4,559.31

See margin.

12e.

y x1,029.43 10,812.735 2 1

y x x40.85 580.08 9,914.0325 2 2 1

y x x x1.08 22.98 662.48 10,006.942 25 2 2 2 1

y x x

x

12h. 2.81 10.04

857.63 35,147.

3 25 2 2 2

1

y x xg12 . 90.18 231.99

34,025.63

25 2 2 1

y xf12 . 1,945.42 39,737.055 2 1

$35,000

18 years

$4,065.22

$38,174.09

See margin.

See margin.

See margin.

See margin.

TEACHExercises 11 and 12 Once the data have been entered into the calculator, the regression equations are easy to determine. Use the regression keystroke sequence that enters the equations into Y1, Y2, and Y3, respectively, so that those equations are not overwritten, and students can easily refer to them.

ANSWERS11e.

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3-5 Credit Cards 179

What Do I Need to Know to Use Credit Cards?Credit cards were introduced in the 1950s. A credit card is a plastic card that entitles its holder to make purchases and pay for them later. The issuer of the card has given the person whose name is on the account a line of credit. The account holder of a credit card has signed an agreement to pay for any purchase made using the card.

Credit cards are so prevalent today that they seem more popular than cash. Businesses that honor credit cards think that consumers spend more money when they just have to sign their names. It is mentally different than removing cash from your wallet when paying for something.

The use of credit cards probably increases impulse buying. Impulse buying is when a consumer purchases something to which they suddenly were attracted to and had no intention of buying. The convenience of using credit cards can also attract new customers to stores that accept them. Credit cards have turned online shopping into a regular habit. Consumers enjoy many advantages when using a credit card.

• There is no need to carry large sums of cash.• Responsible use of a card helps a credit rating (FICO score).• Customers receive or have access to a written record of all purchases.• Some cards have rewards programs such as frequent-flyer miles or

“cash-back” programs.There are two types of credit card accounts. The most commonly used is the

revolving charge account. This means that the entire bill does not have to be paid in full each month. There is a minimum monthly payment, and there is a finance

Objectives • Define the basic vocabulary of credit

cards.• Compute an average daily balance.

Key Termscredit cardimpulse buyingrevolving charge account

charge cardTruth-in-Lending ActSchumer BoxFair Credit Billing ActFair Debt Collection

Practices Actdebit cardElectronic Funds Transfer

Actaverage daily balance

3-5 Credit Cards

Warm-UpA company has 50 employees. Forty of them earn $100 per day, and 10 earn $60 per day. What is the average daily salary of the 50 employees?

Life was a lot simpler when what we honored was father and mother rather than all major credit cards.—Robert Orben, American comedy writer

$92

EXAMINE THE QUESTIONStudents have seen many people use credit cards in stores, but they know very little about the chain of events that using that card has started. They may not see people paying credit card bills, checking monthly statements, or dealing with problems. There is much more to using the cards than just saying, “Charge it!”

CLASS DISCUSSIONA charge card is a type of credit card. However, with a charge card, the credit is not extended over a long period of time.

Stores accept credit cards as a means to attract customers. Ask students how this would attract customers.

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charge the month following any month the bill is not paid in full. Customers have the convenience of stretching out payments over as many months as they choose. However, the interest costs for doing this are relatively high. Popular revolving charge accounts include Visa, MasterCard, Discover Card, and some American Express cards.

A charge card is a special type of credit card. Unlike the cards with revolving charge accounts described above, the monthly bill for all purchases must be paid in full. There is no interest charged. Popular charge cards used today include certain types of American Express cards. Most people informally use the words charge card and credit card interchangeably.

Using credit cards is both a convenience and a responsibility. There is a great temptation to overspend. Cards can be lost or stolen. The Truth-in-Lending Act protects you if your card is lost or stolen. If this happens, notify the creditor who issued the card immediately. You may be partially responsible for charges made by unauthorized users of cards you lose. The maximum liability is $50. You are not

responsible for any charges that occur after you notify the creditor.

If the card number, and not the actual card, is stolen, you are not responsible for any purchases. It is the responsibility of the person selling the merchandise to make sure the purchaser is actually the card owner. The Truth-in-Lending Act also requires all creditors to disclose key information about the credit card fees in the same exact format so consumers can easily read it and compare credit cards. This information is in a box on the credit card bill called the Schumer Box (after Senator Chuck Schumer, who sponsored the legislation). On the left is an example of a Schumer Box.

Cardholders receive a monthly statement of their purchases and any payments they made to the creditor. The Fair Credit Billing Act protects you if there are any errors in your monthly statement. It is your responsibility to notify the creditor about the error. You do not have to pay the amount that is disputed or any finance charge based on that amount until the problem is cleared up.

If you find yourself unable to meet payments required by a creditor, notify that creditor immediately. The Fair Debt Collection Practices Act prohibits the creditor from

Annual MembershipFee

Credit Card Tips fromthe consumerFinancial ProtectionBureau

Minimum InterestCharge

How to Avoid PayingInterest on Purchases

Penalty APR andWhen it Applies

Overdraft AdvanceAPR

Cash Advance APR

Balance TransferAPR

Purchase AnnualPercentage Rate(APR)

INTEREST RATES AND INTEREST CHARGES

19.5%. This APR will vary with the market based on the Prime Rate.b19.5%. This APR will vary with the market based on the Prime Rate.b

18.99%. This APR will vary with the market based on the Prime Rate.a

18.99%. This APR will vary with the market based on the Prime Rate.a

30%. This APR will vary with the market based on the Prime Rate.c

The Penalty APR will be applicable to your Account if you:

• fail to make an Minimum Payment by the date and time due (late payment); • make a payment to us that is returned unpaid; or • do any of the above or exceed your credit limit on another account or loan you have with us or any of our related banks.

How Long will the Penalty APR Apply: If your APRs are increased for any of these reasons, the Penalty APR will apply indefinitely.

Your due date will be a minimum of 21 days after the close of each billing cycle. We will not charge you periodic interest on purchases if youpay your entire balance by the due date each month. We will begincharging interest on balance transfers, cash advances, and overdraft advances on the transaction date.

To Learn more about factors to consider when applying for or using acredit card, visit the website of the Consumer Financial ProtectionBureau at http://www.consumerfinance.gov/learnmore.

None

$0 Intro fee for the first year. After that, $100

Either $5 or 3% of the amount of each transfer, whichever is greater.Either $10 or 5% of the amount of each transfer, whichever is greater.

None

Up to $20 if the balance is less than $100; up to $25 if the balance is$100 to less than $250; up to $35 if the balance is $250 or more.Up to $35.Up to $35.

FEES

Penalty FeesLate Payment

Return PaymentReturn Check

Transaction FeesBalance TransfersCash Advances

Foreign Transactions

CLASS DISCUSSIONAsk students about this scenario: You take a friend’s card, use it extensively, and then have the friend report it lost. Is the friend then only responsible for $50? That would be fraud, and with store video cameras generally in use, it would be easy to get caught.

Ask students if any of them, or their older siblings, have debit cards.

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EXAMPLE 2

Credit card companies issue a monthly statement, therefore APR (annual percentage rate) must be converted to a monthly periodic rate. If the APR is 21.6%, what is the monthly finance charge?

SOLUTION

To change to a monthly finance charge, divide the APR by 12. 21.6 12 1.84 5

The monthly APR is 1.8%. This is the percent that will be used to compute the monthly finance charge. There are several methods that credit card companies use to calculate the finance charge. They all begin with the APR and then compute a periodic rate for each billing cycle. For the purposes of this book, we use the monthly periodic rate to calculate the finance charge for a billing cycle.

harassing you or using unfair means to collect the amount owed. As you can see, you need to be knowledgeable to responsibly use credit and charge cards.

Another type of plastic card is known as a debit card. Though it may look the same, a debit card is not a credit or charge card because there is no creditor extending credit. If you open a debit account, you deposit money into your account, and the debit card acts like an electronic check. You are deducting money directly from your account each time you make a purchase using the debit card.

You cannot make purchases that exceed the balance in your debit card account. Keeping a record of your debit card activity is exactly like keeping the check register you learned about in Section 2-1. The Electronic Funds Transfer Act protects debit card users against unauthorized use of their cards. They are not responsible for purchases made with a lost or stolen card after the card is reported missing. At some retailers, when you use a debit card you are charged a fee similar to the fees charged at an ATM.


Revolving charge account credit cards can have high finance charges, so it is important to verify that the finance charge on your monthly statement is correct.

EXAMPLE 1

Frank lost his credit card in a local mall. He notified his creditor before the card was used. However, later in the day, someone found the card and charged $700 worth of hockey equipment on it. How much is Frank responsible for paying?

SOLUTION By the Truth-in-Lending Act, Frank is responsible for paying nothing because he reported it lost before it was used.


Carrie’s credit card was stolen. She didn’t realize it for days, at which point she notified her creditor. During that time, someone charged $2,000. How much is Carrie responsible for paying?


If a monthly statement shows a monthly interest rate of x percent, express the APR algebraically.

TEACHStudents examine the average daily balance and its role in computing finance charges. Highlight the fact that interest rates are usually given as annual rates, and they need to compute a monthly rate to get the monthly finance charge.

EXAMPLE 1All computer cash registers record the time of the purchase, so it is easy for consumers to determine whether they reported the loss before or after the card was used.

CHECK YOUR UNDERSTANDINGAnswer $50, the maximum liability under the Truth-in-Lending Act

EXAMPLE 2Credit card billing is usually done on a monthly basis.

CHECK YOUR UNDERSTANDINGAnswer 12x

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EXAMPLE 3

Rebecca did not pay last month’s credit card bill in full. Below is a list of Rebecca’s daily balances for her last billing cycle.

For 7 days she owed $456.11. For 3 days she owed $1,177.60. For 6 days she owed $990.08. For 9 days she owed $2,115.15. For 5 days she owed $2,309.13.

Find Rebecca’s average daily balance.

SOLUTION The average daily balance is an arithmetic average. The arithmetic average is also called the mean (introduced in Chapter 1). To find this average, you add the balances for the entire billing period and divide by the number of days.Add the number of days in the list to find the number of days in the cycle.

7 3 6 9 5 301 1 1 1 5

There were 30 days in Rebecca’s billing cycle.To find the sum of the daily balances, multiply the number of days by the amount owed. Then add these products.

Total

7(456.11) 3,192.773(1,177.60) 3,532.80

6(990.08) 5,940.489(2,115.15) 19,036.355(2,309.13) 11,545.65

43,248.05

5

5

5

5

5

Divide the total by 30, and round to the nearest cent.

43,248.05 30 1,441.604 <

The average daily balance is $1,441.60.


Last month, Paul had a daily balance of x dollars for 6 days, y dollars for 12 days, w dollars for q days, and d dollars for 2 days. Express the average daily balance algebraically.

The average daily balance is the average of the amounts you owed each day of the billing period. It changes as purchases and payments are made.

Finance charges are not charged if, in the previous month, the revolving charge credit card bill was paid in full. If you pay your card in full every month, you will never pay a finance charge.

EXAMPLE 3If you purchased an item earlier in the billing cycle, you would have a higher average daily balance than if you purchased it later in the billing cycle. People will consider that fact when they make certain purchases.

The average daily balance will be used to find the finance charge. In a month following a month in which the statement was paid in full, there is no finance charge. You can think of this as a no-interest loan— you got to pay for the items you bought a few weeks later, with no interest.

CHECK YOUR UNDERSTANDING

Answer x y qw dq

6 12 220

1 1 1

1

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EXAMPLE 4

Rebecca (from Example 3) pays a finance charge on her average daily balance of $1,441.60. Her APR is 18%. What is her finance charge for this billing cycle?

SOLUTION Finance charges are computed monthly, so the 18% APR must be divided by 12 to get a monthly percentage rate of 1.5%. Take 1.5% of the average daily balance to get the finance charge.You can view this algebraically as a formula. Finance charge

100monthly rate average daily balance5 ( )

Substitute. 5Finance charge 1.5100

(1,441.60)

The finance charge is $21.62.


Steve owes a finance charge this month because he didn’t pay his bill in full last month. His average daily balance is d dollars and his APR is p percent. Express his finance charge algebraically.

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EXAMPLE 4Make sure students understand that if a bill is paid in full, there will be no finance charge the following month.

Also point out that the billing cycle months are not calendar months. Your bill is not a “February” bill; your billing cycle may go from January 11 through February 11. However, many people would still refer to this as their “February” bill.

CHECK YOUR UNDERSTANDING

Answer p

d

0.0112

Students

often forget that they need to divide the percent by 100 because the percent sign is dropped in the algebraic expression.

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Applications

Life was a lot simpler when what we honored was father and mother rather than all major credit cards.—Robert Orben, American comedy writer

1. Interpret the quote in the context of what you learned about credit and charge cards in this section.

2. Janine’s credit card was stolen, and the thief charged a $44 meal before she reported it stolen. How much of this is Janine responsible for paying?

3. Dan’s credit card was lost on a vacation. He immediately reported it missing. The person who found it days later used it, and charged x dollars’ worth of merchandise on the card, where $200.x . How much of the x dollars is Dan responsible for paying?

4. Felix and Oscar applied for the same credit card from the same bank. The bank checked both of their FICO scores. Felix had an excellent credit rating, and Oscar had a poor credit rating.

a. Felix was given a card with an APR of 14%. What was his monthly percentage rate? Round to the nearest hundredth of a percent.

b. Oscar was given a card with an APR of 21%. What was his monthly percentage rate? Round to the nearest hundredth of a percent.

c. If each of them had an average daily balance of $800 for a specific month, and had to pay a finance charge, how much more would Oscar pay than Felix?

5. Vincent had these daily balances on his credit card for his last billing period. He did not pay the card in full the previous month, so he will have to pay a finance charge. The APR is 19.2%.

9 days @ $778.128 days @ $1,876.004 days @ $2,112.5010 days @ $1,544.31

a. What is the average daily balance? Round to the nearest cent. b. What is the finance charge? Round to the nearest cent.

6. Express the average daily balance algebraically given this set of daily balances.

x days @ y dollars w days @ d dollarsr days @ q dollars m days @ p dollars

7. Suzanne’s average daily balance for last month was x dollars. The finance charge was y dollars.

a. What was the monthly percentage rate? b. What was the APR?

8. Jared’s average daily balance for last month was $560. The finance charge was $8.12.

a. What was the monthly percentage rate? b. What was the APR?

TEACHExercises 5 and 6 Exercise 5 will help students do the algebraic representation required for Exercise 6, if they are having trouble.

ANSWERS1. The writer is making a play on

two senses of the word “honor” as a pun. When a store honors a credit card, it just means they accept it as a means of payment. The writer is lamenting what he sees as the replacement of personal interactions with financial transactions.

See margin.

$44

$0

1.67%

1.75%

$0.64

$1,480.78$23.69

xy wd rq mpx w r m+ + +

+ + +

yx

100

yx

100 12

1.45%17.4%

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CODENUMBER OR DATE TRANSACTION DESCRIPTION AMOUNT

PAYMENTAMOUNTDEPOSIT

$

$ BALANCE8/4

8/5

8/7

8/7

8/7

Baseball Bat

Gas

Deposit

Gas

Dinner at Spooner’sOn the Beach

92 19

51 00

25 00

71 12

FEE�

400 00

778.1992.19a.51.00b.

400.00c.

25.00d.71.12e.

8/11 Books for Fall Semester 491 51 491.51f.

9. Irina’s credit card has an APR of 16.8%. She never pays her balance in full, so she always pays a finance charge. Her next billing cycle starts today. The billing period is 30 days. Today’s balance is $712.04. She is only going to use the credit card once this month, to make a $5,000 down payment on a new car.

a. If she puts the down payment on the credit card today, what will her daily balance be for each of the 30 days of the cycle?

b. Find her average daily balance for the 30-day period if she puts the down payment on the credit card today. Round to the nearest cent.

c. Find the finance charge for this billing period based on the average daily balance from part a. Round to the nearest cent.

d. Find her average daily balance for the 30-day period if she puts the down payment on the credit card on the last day of the billing cycle. Round to the nearest cent.

e. Find the finance charge on the average daily balance from part d. Round to the nearest cent.

f. How much can Irina save in finance charges if she makes the down payment on the last day, as compared to making it on the first day?

10. Gino has a debit card. The account pays no interest. He keeps track of his purchases and deposits in this debit card register. Find the missing entries a–f.

11. Ron did not pay his credit card bill in full last month. He wants to pay it in full this month. On this month’s bill, there is a mistake in the average daily balance. The credit card company lists the average daily balance on his bill as $510.50. Ron computed it himself and found that it is $410.50.

a. The APR is 18%. What finance charge did the credit card company compute on Ron’s bill?

b. If Ron’s average daily balance is correct, what should the finance charge be?12. The terms of Medina’s credit card state that the APR is 17.4%, and if a

payment is not received by the due date, the APR will increase by w percent. The credit card company received Medina’s payment 3 days after the due date in February. Write the interest rate, in decimal form, that she will be charged in March, assuming she carried a balance from February.

$5,712.04

TEACHExercise 9 This exercise highlights the classic manipulation of the billing cycle. If you make a purchase right after the billing period ends, it will not appear on a statement for about a month.

Exercise 10A debit card is not a loan, since you are taking money out of your own account. Although the plastic card and the purchase process seem similar, it is actually a very different process.

ANSWERS10. a. $686.00

b. $635.00c. $1,035.00d. $1,010.00e. $938.88f. $447.37

$5,712.04

$79.97

$878.71

$12.30

$67.67

See margin.

$7.66$6.16

0.0145 1 0.01w

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14. Jill’s credit card was stolen. The thief charged a $900 kayak on the card before she reported it stolen.

a. How much of the thief ’s purchase is Jill responsible for? b. Jill’s average daily balance would have been $1,240 without the thief ’s

purchase. What was the sum of her daily balances for the 30-day billing period? Explain.

c. The thief ’s purchase was on her daily balances for 10 out of the 30 days during the billing cycle. What was the sum of Jill’s daily balances with the thief ’s purchase included?

d. What was the average daily balance with the thief ’s purchase included? Round to the nearest cent.

15. Kristin’s credit rating was lowered, and the credit card company raised her APR from 14% to 15.2%. If her average daily balance this month is x dollars, express algebraically the increase in this month’s finance charge due to the higher APR.

16. It is important to check your credit card bill each month. In the next section, you will carefully examine a credit card statement and learn how to look for errors. Most people would notice a major, expensive purchase that they did not make. A smaller, incorrect charge of $6, for example, might go unnoticed unless the entire statement was checked with a calculator. If 1 million credit card holders were each overcharged $6 each month for 5 years, what would be the total amount that debtors were overcharged, not including the extra finance charges?

17. Naoko has these daily balances on his credit card for September’s billing period. He paid his balance from the August billing in full. 2 days @ $99.78 15 days @ $315.64 11 days @ $515.64 2 days @ $580.32

a. His APR is 15.4%. How much is the finance charge on his September bill? Round to the nearest cent.

b. Does the credit card company need to calculate his average daily balance? Explain.

c. Naoko calculated his average daily balance to be $377.85. Is he correct? If not, what was his average daily balance?

d. What mistake did Naoko make when calculating his average daily balance?

13. Express the missing entries in the debit card register algebraically.

CODENUMBER OR DATE TRANSACTION DESCRIPTION AMOUNT

PAYMENTAMOUNTDEPOSIT

$

$ BALANCE12/3

12/6

12/7

12/11

12/12

Arloff ’s Gifts

Bonnie’s Boutique

Gas

Cable TV

x

yv

FEE�

a.

b.

c.

d.

r e.12/14 Gas g

f.

Deposit

z

m

ANSWERS13. a. m – x

b. m – x – zc. m – x – z – yd. m – x – z – y – ve. m – x – z – y – v + rf. m – x – z – y – v + r – g

14b. $37,200; multiply the average by the number of days.

17b. Because Naoko paid his balance in full, there will be no finance charges. The average daily balance is used to calculate finance charges, so the average daily balance will not be needed.

17d. He only added the four given balances and divided by 4, instead of multiplying the balances by the number of days before adding and correctly dividing that sum by 30.

$50

See margin.

$46,200

$1,540

0.001x

$360 million

$0

See margin.

No; $392.23

See margin.

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3-6 Credit Card Statement 187

What Information Does a Credit Card Statement Give You?Credit cards can be used when making purchases in person, by mail, by phone, online, and more. In most situations you get a receipt for each transaction, but it can be difficult to keep track of the transactions over a billing cycle.

A billing cycle is a predetermined amount of time set by the credit card company that is used for calculating your credit card bill. This cycle can be adjusted by the company based on your creditworthiness. For example, a college student with little or no track record of being able to keep up credit card payments may initially be given a 21-day billing cycle. A seasoned credit card holder who has proven to be financially responsible might get a longer billing cycle.

Throughout your billing, the credit card company takes an accounting of your credits and debits. You may choose to get information about your account online at your convenience, or wait till the company generates that information in the form of a credit card statement at the end of your billing cycle. You should read the statement carefully and verify the charges. All credit card companies have a process through which the credit card holder can dispute errors on the statement.

Jane Sharp has a FlashCard revolving credit card. At the end of a 30-day cycle, Jane receives her FlashCard statement listing all of her purchases and the payments the company has received during that 30-day cycle. Jane’s credit card statement is shown on the next page.

Objective • Identify and use the various entries

in a credit card statement.

Key Termsbilling cyclecredit card statementaccount numbercredit lineavailable credit

billing datepayment due datetransactionsdebit/creditprevious balancepayments/creditsnew purchaseslate chargefinance chargenew balanceminimum payment

3-6 Credit Card Statement

Warm-UpExpress 15% of the difference between x and y algebraically.

Credit cards are like snakes: Handle ’em long enough, and one will bite you.—Elizabeth Warren, U.S. senator

average daily balancenumber of days in billing cyclemonthly periodic rate

0.15 |x−y|

EXAMINE THE QUESTIONMost students have never seen a credit card statement, so the answer to this question will evolve as the lesson progresses. Ask them what information they might find useful on a credit card statement at the end of a monthly cycle. Keep their responses at hand so that you can compare them with the actual information contained on the statement.

CLASS DISCUSSIONAfter reading the introductory material, ask students how the credit card company might benefit from a shorter billing cycle for a college student who has yet to establish a credit history.

Discuss possible errors that a credit card user might find on the credit card statement. For example, double-charging for a single purchase, failure to post a credit, transposition of digits in a purchase, or posting of an incorrect amount.

Have students research how they can establish credit responsibly.

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Locate each of the terms explained below on Jane’s statement.

1. 1.

PreviousSUMMARY

$150.50

BalancePayments/ Credits

New LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$75.00 $284.45 $0.00 $3.53 $363.48 $20.00

TRANSACTIONS

2 Jan Candida’s Gift Shop

3 Jan Skizza’s Pizzas

DEBITS / CREDITS (�)

$75.00

$31.85

5 Jan Beekman Department Store

10 Jan Festival Book Store

$139.10

$38.50

21 Jan Payment �$75.00

AverageDaily

# Daysin Billing APR

MonthlyPeriodic

Balance Cycle Rate

$235.10 30 18% 1.5%

ACCOUNT INFORMATION

Account Number 2653 8987 6098 Billing Date 23 Jan Payment Due 2 Feb

Total Credit LineTotal Available Credit

$ 8,000.00$ 7,636.52

Jane Sharp 25 Main Street Sunrise, NY

Purchases

• Account number Each credit card account has a unique number.• Credit line The maximum amount you can owe at any time.• Available credit The difference between the maximum amount you can owe

and the actual amount you owe.• Billing date The date the bill (statement) was written.• Payment due date The date the monthly payment must be received by the

creditor.• Transactions Lists where purchases were made and the date. Some

companies use the date posted, which indicates when the creditor received its notification of the charge and processed it. Some companies list the date of transaction, which shows when purchases were made or payments were received. Some companies list both the posted and the transaction dates.

• Debits/credits A debit is the amount charged to your account. A credit is a payment made to reduce your debt. Credits are identified by a negative (2) sign or the amount in parentheses.

• Previous balance Any money owed before the current billing period.• Payments/credits Total amount received by the creditor.• New purchases The sum of purchases (debits) on the current bill.• Late charge The penalty for late payments from a previous month.• Finance charge The cost of using the credit card for the current billing

period if not paid off in full.• New balance The amount you currently owe.• Minimum payment This amount is the lowest payment the credit card

company will accept for the current billing period.• Average daily balance The average amount owed per day during the billing

cycle.• Number of days in billing cycle The amount of time, in days, covered by the

current bill.• Monthly periodic rate The APR divided by 12.

CLASS DISCUSSIONThe list of terms included here may seem overwhelming to students. Take your time when explaining them. The terms are critical to the understanding of the credit card process.

Emphasize that it is important to know what the dates on your statement refer to.

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Here you learn how to read and verify entries on a credit card statement.

PreviousSUMMARY

$150.50


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$75.00 $284.45 $0.00 $3.53 $363.48 $20.00

NewPurchases

TRANSACTIONS

2 Jan Candida’s Gift Shop

3 Jan Skizza’s Pizzas

DEBITS / CREDITS (2)

$75.00

$31.85

5 Jan Beekman Department Store

10 Jan Festival Book Store

$139.10

$38.50

21 Jan Payment 2$75.00

ACCOUNT INFORMATION

Account Number 2653 8987 6098 Billing Date 23 Jan Payment Due 2 Feb

EXAMPLE 1

The summary portion of Jane Sharp’s credit card statement shown on the previous page looks as follows:

a. Explain how the new purchases amount was determined.b. Explain how the new balance amount was determined.

SOLUTION

a. The new purchases amount is the sum of the purchases, which also appear as debits. This sum must equal the amount $284.45 listed in the New Purchases section of the statement summary.

5 1 1 1 5New purchases 75 31.85 139.10 38.50 $284.45b. The new balance amount is determined by using the formula given below.

Previous 2 Balance

Payments/Credits

1 New Purchases

1 Finance Charge

1 Late Charge

5 New Balance

150.50 2 75 1 284.45 1 3.53 1 0 5 $363.48


Suppose you create the following spreadsheet that models the statement summary and input the values in row 2. Write the spreadsheet formula to compute the new balance in cell F2.

A B C D E F

1Previous Balance Payments

New Purchases Late Charge

Finance Charge

New Balance

2

TEACHDisplay a list of the terms introduced in this lesson. Ask students to write as many definitions as they are able with the current knowledge that they already have about credit. Use their definitions as a springboard to giving more precise meanings to the terms.

EXAMPLE 1This problem begins the unwrapping process that will help students understand how a credit card statement is built. The “New Purchases” are the sum of the purchases made during the cycle. A number of things contribute to the “New Balance.” If there is a carryover balance from the previous month, begin with that amount. Note that the carryover balance necessitates a finance charge. If there is no carryover balance, there will be no finance charge on the new purchases for that cycle. A late charge is added if the payment from the last cycle arrives late. You might want to discuss the benefits of online payments in avoiding late charges.

CHECK YOUR UNDERSTANDINGAnswer =A2–B2+C2+ D2+E2

If there is no entry in any cell, the spreadsheet will use a zero amount in the calculation.

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Rhonda had a previous balance of $567.91 and made an on-time credit card payment of $567.91. She has a credit line of x dollars and made purchases totaling y dollars. Write an algebraic expression that represents her current available credit.

PreviousSUMMARY

$1,748.00


LateCharge

FinanceCharge

NewBalance

�$100.00 $800.00 $9.15 $19.00 $2,576.15

NewPurchases

EXAMPLE 3

Myrna is examining the summary section of her credit card statement. Myrna has checked all the entries on her bill and agrees with everything except the new balance. Determine where the error was made.

SOLUTION Add the amounts that show Myrna’s debits.

$1,748.00 previous balance

800.00 purchases

9.15 finance charge

1 19.00 late charge

$2,576.15 total to be paid

Subtract the $100 payment/credit, and Myrna’s new balance will be $2,476.15. It appears that Myrna was not credited for her payment. Under the Fair Credit Billing Act, Myrna must notify her creditor in writing within 60 days from the statement date on her bill.

Previous

SUMMARY$850.00Balance

Payments/ Credits

LateCharge

FinanceCharge

NewBalance

$300.00

$3.00 $4.78 $507.78

NewPurchases

�$560.00


Determine the error that was made using the following summary statement.

EXAMPLE 2

Pascual has a credit limit of $15,000 on his credit card. His summary looks as follows. How much available credit does Pascual have?

SOLUTION Pascual needs to determine his new balance and then subtract that from his credit line in order to find his available credit.

4,598.12 4,000.00 1,368.55 20.00 5.78 1,992.452 1 1 1 5

He has a new balance of $1,992.45. Subtracting this from his credit line of $15,000 leaves him with an available credit of $13,007.55.

PreviousSUMMARY

$4,598.12


LateCharge

FinanceCharge

�$4,000.00 $1,368.55 $20.00 $5.78

NewPurchases

EXAMPLE 2Since a credit line is the maximum amount that a creditor is willing to lend, the available credit is the amount available to the after the debits have been subtracted from the credit line.

CHECK YOUR UNDERSTANDINGAnswer x – y

Students can use Example 2 as a guide to find the solution.

EXAMPLE 3This problem offers students an excellent example of why every credit card statement must be checked for accuracy. Initially, it looks as if the statement is correct, since the total to be paid and the new balance listed on the statement match. But the $100 payment has not been credited to the account. Therefore, the actual new balance should be $100 less than stated. Discuss the Fair Credit Billing Act as a means of protecting consumers from this type of error.

Explain to students that faxes, e-mails, and texts are not acceptable as written notification of an error on a bill by many lending institutions. But a number of lending institutions do have ways to make a claim about an error directly on their websites.

CHECK YOUR UNDERSTANDINGAnswer The new balance should be $597.78.

It appears that the payment of $560 was recorded as $650.

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Applications

Credit cards are like snakes: Handle ’em long enough, and one will bite you. —Elizabeth Warren, U.S. senator

1. How might the quote apply to what you have learned? Use the FlashCard statement to answer Exercises 2–7.

PreviousSUMMARY

$420.50


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$150.00 $1,227.24 $0.00 $19.80 $1,517.54 $30.00

TRANSACTIONS

9 MAY 3291684271

12 MAY 594683219


$975.00

$32.50

15 MAY 7677095385

18 MAY 8765713281

$178.21

$41.5321 MAY 321447162

2$150.00

AverageDaily


MonthlyPeriodic

Balance Cycle Rate

$1,199.97 30 19.8% 1.65%

ACCOUNT INFORMATION

Account Number 4-10700000 Billing Date 30 May Payment Due 8 Jun


$ 3,000.00$ 1,661.51

Fanelli Furs

Brooklyn Pets

Maple Garage

PAYMENT

Caruso’s Restaurant

NewPurchases

2. How many purchases were made during the billing cycle?3. What is the sum of all purchases made during the billing cycle?4. When is the payment for this statement due?5. What is the minimum amount that can be paid?6. How many days are in the billing cycle?7. What is the previous balance?8. Rollie has a credit card with a credit limit of $4,000. He made the following

purchases: $425.36, $358.33, $377.11, and $90.20. What is Rollie’s available credit?

9. Rebecca has a credit limit of $6,500 on her credit card. She had a previous balance of $398.54 and made a $250 payment. The total of her purchases is $1,257.89. What is Rebecca’s available credit?

10. The APR on Leslie’s credit card is currently 21.6%. What is the monthly periodic rate?

11. Sheldon’s monthly periodic rate is 1.95%. What is the APR?12. Zea has a credit limit of $2,000 on her credit card. Each month, she charges

about $200 and makes a payment of $125. a. Estimate the number of months that Zea can continue this pattern until

she reaches her credit limit. b. Consider that part of the $125 Zea pays each month will be for finance

charges. How will the number of months from part a be affected by these charges?

TEACHHave students work on Exercises 2–7 with a partner or in a small group. Walk around the room listening to the discussion that ensues. Misconceptions about terms and procedures may surface that you will need to address before assigning any further exercises.

Exercises 2–7Exercises 2–7 lead students through the completion of the statement through a guided approach. An incorrect answer in the early stages here could affect the subsequent answers.

ANSWERS1. Senator Warren warns us of

the potential dangers of credit cards. Suggests that credit cards are intended to take advantage of consumers.

4

$1,227.24

$30

June 8

30

$420.50

$2,749

$5,093.57

1.8%

23.4%

27

The number of months will be less than 27.

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13. Examine this portion of the credit card summary.

a. Express the sum of the cycle’s daily balances algebraically.

b. Express the monthly periodic rate as an equivalent decimal without the % symbol.

14. Fill in the missing amounts for a–d.

AverageDaily


Balance Cycle

W X Y %

PreviousSUMMARY

$215.88


LateCharge

FinanceCharge

NewBalance

MinimumPayment

a. b. $0.00 $6.70 c. $25.00

TRANSACTIONS

6 AUG Meghan’s Shop

7 AUG Payment


$85.63

$855.00

8 AUG Joe’s Italian Restaurant

10 AUG University of New York

$47.60

$370.5015 AUG SkyHigh Airlines

2$63.00

AverageDaily


MonthlyPeriodic

Balance Cycle Rate

$446.41 30 18% 1.5%

ACCOUNT INFORMATION

Type Revolving Account Number 234 98765 90 Billing Date 16 Aug Payment Due Date 1 Sep


$ 5,000.00d.

16 AUG Payment 2$137.00

NewPurchases

15. Examine the summary section of the monthly credit card statement below. Use the first five entries to determine whether the new balance is correct. If it is incorrect, write the correct amount.

PreviousSUMMARY

$424.41


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$104.41 $103.38 $23.00 $7.77 $454.15 $54.00

NewPurchases

PreviousSUMMARY

$359.02


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$80.00 $103.65 $0.00 $5.34 $548.01 $18.00

NewPurchases

16. Check the new balance entry on the monthly statement below by using the first five entries. If the new balance is incorrect, write the correct amount.

17. A credit card statement is modeled by the following spreadsheet. Entries are made in columns A–F. Write the formula to calculate the available credit in cell G2.

A B C D E F G

1Previous Balance Payments

New Purchases

Late Charge

Finance Charge

Credit Line

Available Credit

2

PreviousSUMMARY

$939.81


LateCharge

FinanceCharge

NewBalance

MinimumPayment

$125.25 $3.00 $15.38 $833.44 $25.00

NewPurchases

18. Determine the amount of the payment made on the following credit card.

19. The previous balance after the last billing cycle is represented by A, recent purchases by B, payments by C, finance charge by D, late charge by E. Express the relationship among the variables that must be true in order for the new balance to be $0.00.

TEACHExercises 14–18 This cluster of exercises focuses on the summary section of the credit card statement. Consider completing Exercise 13 with the entire class before assigning the remaining problems.

ANSWERS14a. $20014b. $1,358.7314c. $1,381.3114d. $3,618.69

WX

y1200

See margin.

Incorrect; it should be $388.01

Correct

$250

=F2−(A2−B2+C2+D2+E2)

A 1 B 1 D 1 E = C

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3-7 Average Daily Balance 193

How Are the Entries on the Monthly Statement Calculated?Credit card users who do not pay their bills in full are charged a finance charge for the convenience of extra payment time. The finance charge is computed on any statement in which the consumer has a previous unpaid balance.

The finance charge is based on the average amount the consumer owed each day of the billing cycle, the average daily balance. Average daily balance is used with the monthly periodic rate to determine the finance charge. Billing cycles and interest rates differ from card to card and from user to user with the same credit card.


Here you learn how to calculate the average daily balance using a credit card billing calendar, often called a credit calendar. A credit calendar is a visual accounting of the purchases, payments, and balances for each day of the billing cycle.

Objectives • Calculate the average daily balance

using the credit calendar.• Calculate the finance charge using

the credit calendar.

Key Termscredit calendarbilling dateMinimum Payment

Warning Boxnegative amortization or

NegAm

3-7 Average Daily Balance

Warm-UpThe scores 4, 6, x, 8, 10 are written in ascending order. Find the value of x if the mean of the set equals the median.

The best way to deal with credit card debt is to educate yourself.—Mark Rosen, author

© ja

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EXAMINE THE QUESTIONIn this lesson, students will learn how the average daily balance is determined and then used in the calculation of a finance charge.

CLASS DISCUSSIONMake available to students the “Terms and Conditions” section of a cardholder agreement. Students will be able to see why many cardholders skip this information. Look for paragraphs where “average daily balance” or “daily balance” are mentioned.

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EXAMPLE 1

Use the information given in Elena Kaye’s credit card statement to verify the accuracy of her average daily balance.

SOLUTION Carefully follow Steps 1–8.

Elena Kaye 44 Central Avenue Onesburg, TX

PreviousSUMMARY

$829.30


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$160.00 $122.00 $0.00 $12.09 $803.39 $59.00

TRANSACTIONS

25 Oct House Depot

29 Oct Bubble Wrap Shipping Co.


$67.00

$55.00

5 Nov Payment 2$160.00

AverageDaily


MonthlyPeriodic

Balance Cycle Rate

854.46 31 16.98% 1.415%

ACCOUNT INFORMATION

Account Number 07-3458-1299 Billing Date 13 Nov Payment Due 5 Dec


$ 3,000.00$ 2,196.61

NewPurchases

Step 1 On a blank sheet of paper, draw a grid that has seven boxes across and five boxes down. Draw an arc in each corner.

OCT.

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31 1 2 3

4 5 6 7 8 9 10

11 12 13

NOV.

Step 2 On Elena’s statement you can find that the number of days in the billing cycle is 31 days. Shade in the last 4 days that will not be used.

Step 3 Enter the billing date, 11/13, in the corner section of the last day on the calendar. Number the days back from that date until the calendar is completely filled in. Notice that although the billing date is in November, the billing cycle includes some days from October. Enter the month of the first date in your calendar and the month of the first day of the next month.

EXAMPLE 1Distribute copies of the blank credit calendar, which can be found at www.cengage.com/financial_alg2e, and also project it for students to see. Carefully work through each of the steps with students. As you mark the template, they should be doing the same with their own copy.

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OCT.

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31 1 2 3

4 5 6 7 8 9 10

11 12 13

NOV.

+67.00

+55.00

–160.00

Step 4 Look at the posted dates of each of the charges (debits). Put a plus sign (1) and the charged amount on the calendar dates that have debits posted. Next look at the posted date of the payment made. Put a minus sign (2) and the payment made on that calendar date.

Step 5 The first day of the billing cycle is October 14. The previous balance of $829.30 is the amount Elena owed on October 14. Enter that balance on October 14. Notice that Elena made no purchases or payments until October 25, so on each day from October 14 to October 24, the daily balance is $829.30. Enter this number on each of these dates.

OCT.

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31 1 2 3

4 5 6 7 8 9 10

11 12 13

NOV.

+67.00

+55.00

–160.00

$ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30

$ 829.30 $ 829.30 $ 829.30 $ 829.30

OCT.

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31 1 2 3

4 5 6 7 8 9 10

11 12 13

NOV.

+67.00

+55.00

–160.00

$ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30

$ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 896.30 $ 896.30 $ 896.30

$ 896.30

OCT.

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31 1 2 3

4 5 6 7 8 9 10

11 12 13

NOV.

+67.00

+55.00

–160.00

$ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 829.30

$ 829.30 $ 829.30 $ 829.30 $ 829.30 $ 896.30 $ 896.30 $ 896.30

$ 896.30 $ 951.30 $ 951.30 $ 951.30 $ 951.30 $ 951.30 $ 951.30

$ 951.30 $ 791.30 $ 791.30 $ 791.30 $ 791.30 $ 791.30 $ 791.30

$ 791.30 $ 791.30 $ 791.30

Step 6 A $67.00 purchase was made on October 25. The amount Elena owes on October 25 is increased by $67.00. The amount owed from October 25 to October 28 is $896.30.

Step 7 A $55.00 purchase was made on October 29, and a payment of $160.00 was made on November 5. The purchase must be added to the daily balance of October 28, and the payment must be subtracted from the daily balance of November 4. There are no other transactions, so continue the daily balance amount through to the end of the billing cycle.

Step 8 To find the average daily balance, add all the daily balances and divide by the number of days in the billing cycle, 31. The sum of the daily balances is $26,488.30. Divide that sum by 31.

26,488.30 31 854.464 5

The average daily balance is $854.46.


Is there a better time during the billing cycle when Elena could have made her payment so that the average daily balance would have been less?

CHECK YOUR UNDERSTANDINGAnswer Students should understand that the closer the payment is made to the beginning of the cycle, the lower the average daily balance will be for that cycle.

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EXAMPLE 2

Determine the finance charge for Elena’s billing cycle.

SOLUTION Because Elena did not pay off her balance in full for the previous month, she will be paying a finance charge this month. Once the average daily balance is computed using the calendar, find the finance charge using the average daily balance and the monthly periodic rate.

Balance 3 monthly periodic rate 854.46 1.415%3

Express rate as a decimal. 854.46 0.01415%3

Simplify and round. 12.09Her finance charge is $12.09.


When might Elena have made her purchases during the billing cycle in order to decrease her finance charge?

Minimum PaymentIn 2009, President Barack Obama signed the Credit Card Accountability, Responsibility, and Disclosure Act (Credit CARD Act). Credit card issuers were required to include a box on the credit card statement to show how long it would take for the balance to be paid off if only the minimum payment was made and no extra charges put on the account. This is known as the Minimum Payment Warning Box. Most major credit card issuers use one of these two methods for determining the minimum monthly payment:

• 2% of the balance; or• 1% of the balance plus all interest and fees

The Credit CARD Act also required that the minimum payment amount had to be enough so that part of it would be applied to paying down the debt. Before the Credit CARD Act, this had not always been the case, as you see in the next example.

EXAMPLE 3

Alex found an old credit card statement that was sent to him before the enactment of the Credit CARD Act. He had no previous balance but charged $4,000 that month. His credit card account has a monthly percentage rate of 1.5%. He made no additional purchases during that billing cycle. A minimum of $20 was required as a monthly payment. How long would it have taken Alex to pay down his debt if he continued to only pay the minimum amount without making any other credit card purchases?

SOLUTION Let’s walk through a few months to see the status of Alex’s credit card account. Alex pays the $20 minimum payment and carries over a balance of $3,980. At the end of the next billing cycle, he must pay 1.5% of what is owed.Calculate the interest owed that month. 3,980 0.015 59.703 5

Alex owed $59.70 in interest that billing cycle. After making a minimum payment of $20, determine the balance that will be carried over to the next cycle.

EXAMPLE 2It is important for cardholders to read the fine print on their statements. Companies vary in how they calculate the periodic rate. For the purposes of this text, we use the monthly periodic rate. Some credit card statements include the monthly periodic rate, whereas others do not. If the rate is missing, it is necessary for students to calculate the MPR by dividing the APR by 12. Then they express the MPR as an equivalent decimal and multiply that amount times the average daily balance.

CHECK YOUR UNDERSTANDINGAnswer The later in the billing cycle purchases are made, the lower the average daily balance, which results in a lower finance charge.

TEACHHave students do an online search for information about the CARD Act. Discuss the provisions and why the government felt that it was necessary to enact.

EXAMPLE 3This is a very important example. It shows students how some unscrupulous companies would take advantage of the fact that very few cardholders understood the mathematics of the minimum payment. These cardholders mistakenly thought that they were paying down their balances by only making the minimum payment, but they were wrong. This is a glaring example of why consumers should be educated consumers.

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From the sum of the previous balance and the interest, subtract the payment. 3,980 59.70 20 4,019.701 2 5

Alex carries over a balance of $4,019.70. Let’s try this for one more billing cycle. Find 1.5% of the balance. Add that to the total owed and subtract the minimum payment of $20.

4,019.70 0.015 60.303 <4,019.70 60.30 20 4,0601 2 5

The balance carried over to the next billing cycle is $4,060. What do you notice about the consecutive month’s balances? Rather than paying down the debt, the balances are increasing. By paying the minimum amount each month, Alex has no chance of paying down his credit card debt. This is known as negative amortization, or NegAm. Basically, in a NegAm situation, the minimum payment is less than the interest that is being charged, so the amount owed increases rather than decreases. The government recognized that credit card issuers were making a profit by leading people to believe they would eventually pay down the debt by paying only the required minimum. The Credit CARD Act put an end to that practice. The borrower is now assured that the minimum payment will reduce the debt and lead to a payment of what is owed. To make this process clearer to credit card holders, a Minimum Payment Warning Box was added to the credit card statement. A sample of the Minimum Payment Warning Box is shown here below the account information.


Lucas just received his credit card statement. He has a balance of $3,333.67. The Minimum Payment Warning Box states that if he makes only the minimum payment of $35 per month, it will take him 12 years and will pay a total of $6,472. If he makes a monthly payment of $116, it will take 3 years to pay off the balance and he will have paid a total of $4,193. What will be the percent increase in total payments if Lucas only pays the minimum rather than $116 per month?

New BalanceMinimum Payment Due

Minimum Payment Warning: If you make only the minimum payment each period,you will pay more in interest and it will take you longer to pay off your balance. Forexample.

If you make no additionalcharges and each month you pay...

You will pay off the balanceshown on this statement inabout...

Only the Minimum Payment Due 3 years $ 1,324

And you will pay anestimated total of...

$1,053.38$35.00

This informs the consumer that by making only the minimum payment each cycle, the total amount owed will be paid off in 3 years. Some credit card companies add another line to the box indicating how much can be saved in interest and time if slightly more than the minimum amount is paid per month.

CHECK YOUR UNDERSTANDINGAnswer 54.4% increase

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Applications

1. How might the quote apply to what you have learned?2. Ralph just received his June FlashCard bill. He did not pay his May bill in full,

so his June bill shows a previous balance and a finance charge. The average daily balance is $470, and the monthly periodic rate is 1.5%. What should Ralph’s finance charge be?

3. Lauren did not pay her January FlashCard bill in full, so her February bill has a finance charge added on. The average daily balance is $510.44, and the monthly periodic rate is 1.3%. What should Lauren’s finance charge be on her February statement?

4. Jennifer did not pay her FlashCard bill in full in September. Her October bill showed a finance charge, and she wants to see whether or not it is correct. The average daily balance is $970.50, and the APR is 15.6%. Find the finance charge for her October statement.

5. Daniyar paid his April FlashCard bill in full. His May bill shows an average daily balance of $270.31 and a monthly periodic rate of 1.65%. What is the finance charge on Daniyar’s May statement?

6. Use Mark Gilley’s FlashCard statement. The average daily balance, finance charge, available credit, and new balance amounts are not filled in. You can find a copy of the blank credit calendar at www.cengage.com/financial_alg2e.

The best way to deal with credit card debt is to educate yourself.—Mark Rosen, author

Mark Gilley 700 West Street Maintown, FL

PreviousSUMMARY

$800.00


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$200.00 $342.00 $0.00 $25.00

TRANSACTIONS

31 May 63214987261

12 Jun 62115497621


$251.00

$72.50

18 Jun 73216532116 2$200.00

AverageDaily


MonthlyPeriodic

Balance Cycle Rate

31 18% 1.5%

ACCOUNT INFORMATION

Account Number 7-6231-491 Billing Date 26 Jun Payment Due 10 Jul


$ 6,000.00

20 Jun 73162225142

Linda’s Art Shop

Artisign’s Inc.

Payment Thank you

Sylvart Corp. $18.50

NewPurchases

a. What is Mark’s average daily balance? b. What is Mark’s finance charge? c. What is Mark’s new balance? d. What is Mark’s available credit? e. If the $200 payment had been posted on 6/13, would Mark’s finance charge

for this billing cycle have been higher or lower?

TEACHExercises 2–4 It is important that students understand the effect that a partial payment has on the following month’s bill. Address this before assigning these exercises.

Exercise 5Since a complete payment was made the prior month, it is not necessary to make any calculations. There will be no finance charge.

Exercise 6Extend this exercise by having students develop a credit card statement that contains one or more errors. Once completed, they can switch with a partner and find the errors.

ANSWERS1. The quote is a warning about

loans and debts. Entering into any debt agreement should be done cautiously and wisely.

$7.05

$6.64

$12.62

See margin.

$0

$999.81$15.00

$957.00$5,043.00

Lower; the ADB would have been lower, so the finance charge would be lower as well.

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7. After Wade paid his May credit card bill, he still had a balance of z dollars. He made no additional payments or purchases before he received his next bill. The monthly periodic rate on this account is 2.015%. What expression represents the finance charge on his June statement?

8. Ed Lubbock’s FlashCard statement is below. There are entries missing.

Ed Lubbock 1234 Algebra Street Euclid, WA

PreviousSUMMARY

$421.50


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$100.00 $78.00 $30.00

TRANSACTIONS

24 NOV 632174293

1 DEC 321446253


$48.00

$30.006 DEC 333261114

2$100.00

AverageDaily


MonthlyPeriodic

Balance Cycle Rate

30 19.8% 1.65%

ACCOUNT INFORMATION

Account Number 7-6234712 Billing Date 10 Dec Payment Due 21 Dec


$ 1,000.00

Rusty’s Rib Palace

Payment

Petrela Sailboats

NewPurchases

a. What is Ed’s average daily balance? b. What is Ed’s finance charge? c. What is Ed’s new balance? d. What is Ed’s available credit? e. If the $30 charge to Petrela Sailboats had been posted on 12/9, would the

finance charge be higher or lower for this billing cycle? Explain.9. Examine the following 21-day credit calendar. The opening balance is Y

dollars. On March 23, a purchase of X dollars was made. On March 28, a payment of Z dollars was made. On April 4, a purchase of W dollars was made.

MARCHY

Y1 X

Y Y Y Y Y Y

APRIL

2 Z

1 W

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30 31 1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

a. What is the algebraic expression for the daily balance on March 23? Write it in on that date and on March 24–27.

b. What is the algebraic expression for the daily balance on March 28 after the payment is made? Write it on that date and on March 29 to April 3.

c. What is the algebraic expression that represents the daily balance on April 4 after the purchase is made? Write it on that date and on April 5.

d. Write the algebraic expression for the sum of the daily balances. e. What is the algebraic expression for the average daily balance?

TEACHExercise 8 This exercise requires students to construct and use a credit calendar. Make sure that they understand the need to alter the calendar depending on the number of days in the cycle. They also need to “date backward,” starting from the billing date listed in the statement. A reminder as to the number of days in a given month may be needed.

Exercise 9This exercise extends the concepts learned in this lesson so that students can model the credit calendar process algebraically. Do not assign this problem until you are sure that students correctly answered Exercise 8 They should be encouraged to model the solution to this problem after the one in Exercise 8.$420.37

$6.94$406.44

$593.56

Lower; ADB is lower

Y 1 X

Y 1 X − Z

Y 1 X − Z 1 WSee margin.

See margin.

ANSWERS9d. 7Y 1 5(Y + X) + 7(Y + X 2 Z) + 2(Y + X 2 Z + W)

0.02015z

9e.(7 5( ) 7( ) 2( ))

211 1 1 1 2 1 1 2 1Y Y X Y X Z Y X Z W

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10. Examine the credit card situations in Exercises 10 and 11. In each case, the credit card holder had no previous balance. The new balance was a result of purchases made that billing cycle. Identify whether or not the borrower can pay off the balance by making only the minimum payment each month. In both instances, no other charges are made to the account. Complete each chart for five billing cycles. Round all amounts to the nearest penny.

a. Balance: $3,220.00 APR 17.52% Minimum Payment $40.00

Previous Balance Interest Balance Minimum Payment

$3220.00 $40.00

$3180.00 a. b. c.

d. e. f. g.

h. i. j. k.

l. m. n. o.

b. Balance: $980.00 APR 14.4% Minimum Payment $20.00

Previous Balance Interest Balance Minimum Payment

$980.00 $20.00

$960.00 a. b. c.

d. e. f. g.

h. i. j. k.

l. m. n. o.

ANSWERS10a. $46.4310b. $3,226.4310c. $4010d. $3,186.4310e. $46.5210f. $3,232.9510g. $4010h. $3,192.9510i. $46.6210j. $3,239.5710k. $4010l. $3,199.5710m. $46.7110n. $3,246.2810o. 40

No, the balance is increasing.

11a. $11.5211b. $971.5211c. $2011d. $951.5211e. $11.4211f. $962.9411g. $2011h. $942.9411i. $11.3211j. $954.2611k. $2011l. $934.2611m. $11.2111n. $945.4711o. $20

Yes, the balance is decreasing.

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Assessment 201

You Write the Story!!FICO scores are measures of your credit risk to a potential creditor. The graph gives the weighted contribution of several factors that affect your credit rating. The Fair Isaac Corporation, the creators of the FICO score, keeps their formulas for computing the scores a secret. Write a short news-type article concerning the circle graph. You can find a copy of this graph at www.cengage.com/financial_alg2e. Copy and paste it into your article.

Chapter 3Assessment

Real Numbers

Examine the equation below used for monthly loan payment calculations. Look through this chapter and your notes to help you write a problem that could be modeled by the equation.

184.7318,000 0.0429

121 0.0429

12

1 0.042912

1

12(10)

12(10)5

1

1 2

Types of Credit and Creditors You Used

The Length of your Credit History

The Amount of Current Debt

Payment History

Recently Obtained Credit Amounts

10%

10%

15%

30%

35%

Reality Check

1. There are several laws that regulate consumer credit in the United States. Find when each act was signed into law. What problem was the act trying to help solve? What are the major provisions of each act? Prepare a poster or project an electronic slide show displaying your findings. The laws are listed below.• Equal Credit Opportunity Act• Electronic Funds Transfer Act• Fair Credit Reporting Act• Fair Credit Billing Act• Fair Debt Collection Practices Act• Truth-in-Lending Act• Credit CARD Act

What’s the Problem?

Encourage students to do a Web search on FICO scores before writing the story. They will notice that the actual formula used to calculate the scores is never stated. The only information given is the percent contributions as depicted in the graph.

See Additional Answers.

REALITY CHECKThe Reality Check projects are excellent opportunities for alternative assessments. They give students an additional avenue to show what they have learned, so their grades are not solely based on tests.

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2. Visit two lending institutions in your area. Find the APR, monthly payment, and total finance charge for a $15,000, 3-year loan at the two lenders. Prepare a poster that includes a business card from each lender and the following mathematical information for the loan.• APR• Monthly payment• Total of all monthly payments• Finance charge

3. Go online and find information on FICO scores. What is the range of possible scores? How can each score be interpreted? What contributes to the FICO score? Summarize the information you find from the websites. Prepare your information in a report.

4. There is a mathematical algorithm that can be used to check if you entered a valid credit card number when you shop online. It is called the Luhn Algorithm. It was created to guard against people entering credit card numbers incorrectly or trying to use false credit card numbers. Go online and find out how the Luhn Algorithm works. Give an example that shows how the algorithm can be used.

5. There are three major credit reporting agencies in the United States. They are named Equifax, Experian, and TransUnion. They keep records of your credit activity and provide your potential creditors with information on your financial habits. This helps a creditor decide how much of a credit risk each customer is. Look up information about these three credit reporting agencies. Summarize the information you obtain in a report.

6. Find contact information for three credit unions in your area. Write to each credit union and explain that you are doing a report for school. Find the requirements to join each credit union. Find the APR, monthly payment, and finance charges for a $31,000 new-car loan over a 5-year period. Prepare your information on a poster.

7. Talk to your teacher about having a local bank representative come to your class. Have the class prepare questions about loans and credit cards in advance. Plan a script of the questions that will be addressed. When the bank representative comes to speak, act as moderator for the discussion. Keep a log of the questions and which student asked them. Write a thank-you letter to the bank representative after the session.

8. Interview your parents or relatives about their use of loans and credit cards. Find out what they consider wise spending habits and what they have learned about credit. If they agree to let you see their last credit card statement, show them how to check entries in the statement, including the average daily balance and the finance charge.

9. Find out if any local store has an installment plan, layaway plan, or deferred payment plan. Go to the store and interview a customer service representative. Ask questions about how their plans work. Get the monthly payment and finance charge for a specific item in the store, purchased under each type of plan. Prepare a report for the class.

10. Find a website that lists the terms and conditions of a major credit card. Research two different cards by going to the provider’s links. Compare and contrast the advantages and disadvantages of each.

11. Some credit card providers offer student credit cards. Research this type of card and discuss how it differs from a regular credit card.

The Reality Check projects in this lesson ask students to do research, go to a lending institution and gather current information, do online searches for credit protection agencies, invite guest speakers into the classroom to make presentations, interview parents or friends about their credit experiences, and more.

Each project is designed so that students can use what they have learned in this chapter as a springboard for further investigation.

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Assessment 203

12. The Schumer Box contains much of a credit card’s “fine print.” Do online research to determine what the Schumer Box looks like and what it contains. Do all lenders have to follow the same format? Find samples of the Schumer Box from different creditors. Make a poster or PowerPoint presentation about your discoveries.

13. In Section 3-3 you learned about student loans. A number of websites were listed there. Go to those websites and write a brief report about how such sites could be helpful to students looking for loan information. Then, select a college, university, or career school. Find out the cost of tuition with room and board for one year. Use the current rate for a Federal subsidized loan, a federal unsubsidized loan, and for a private loan to calculate the total cost of borrowing the entire amount that you researched. Construct a chart comparing the three different types of loans.

14. In this chapter you learned about loans and credit. Do you have a specific interest related to any of the topics discussed? For this project you design your own project assignment based on your interests. Read all of the Reality Check projects to get a basic idea of what comprises a project assignment. When you have decided on a project topic and plan, download the project proposal form at www.cengage.com/financial_alg2e and carefully complete the project information. Create a project assignment for a project you would like to complete. You will need to get it approved by your teacher before undertaking the project. Upon teacher approval, complete the project you have created.

© C

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There are billions of credit cards in use today. Imagine a pile of 1.5 billion credit cards. How far would they stretch end-to-end?

1. A credit card’s length is 85.6 mm. Convert this length to inches using an online metric conversion table. Round to the nearest hundredth.

2. There are 5,280 feet in a mile and 12 inches in a foot. How many inches are in a mile?

3. How many credit cards, placed end to end, would it take to span a mile? Round to the nearest integer.

4. The circumference of Earth is approximately 24,901 miles at the equator. How many credit cards (end-to-end) would it take to circle Earth?

5. Write your answer to Exercise 4 in words.6. In Really? Really! you read facts involving 1.5 billion credit cards. How many

times would 1.5 billion credit cards circle Earth at the equator?

Really? Really! Revisited

In this feature, students get a sense of just what 1 billion credit cards are. They calculate the number of credit cards it would take to circle Earth at the equator. This impressive number and the fact that there are more than enough credit cards in use today worldwide that would accomplish that task should underscore the fact that the use of credit is an integral part of our daily lives.

3.35 inches

63,360 inches

18,913

470,952,613

More than twice

Four hundred seventy million, nine hundred fifty-two thousand, six hundred thirteen

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Assessment 205

Applications

Round monetary amounts to the nearest cent. 1. Faith is taking an $8,100, 2½-year loan with an APR of 3.22%. What is the

monthly payment for this loan? Round to the nearest cent.2. Shania bought a $1,455 drum set on an installment plan. The installment

agreement included a 15% down payment and 18 monthly payments of $80.78 each.

a. How much is the down payment? b. What is the total amount of the monthly payments? c. How much will Shania pay for the drum set on the installment plan? d. What is the finance charge?

3. Pauline’s credit card was lost on a business trip. She immediately reported it missing to her creditor. The person who found it hours later used it and charged w dollars’ worth of merchandise on the card, where w < $50. How much of the w dollars is Pauline responsible for paying?

4. Sal took out a 20-day payday loan from the Just Loans store. He borrowed $350 and is being charged $75 interest. What is the APR for this loan?

5. Carly took a $7,000, 3-year loan with an APR of 3.15%. a. What is the monthly payment? Round to the nearest cent. b. What is the total amount of the monthly payments? c. What is the finance charge?

6. Sarah is taking out a $24,400, 4-year new-car loan with an APR of 2.88%. What is the finance charge for this loan? Round to the nearest hundred dollars.

7. The policy of the Black Oyster Pawnshop is to lend up to 30% of the value of a borrower’s collateral. Pete wants to use a $2,000 guitar and a $900 camera as collateral for a loan. What is the maximum amount that he could borrow from Black Oyster?

8. Rodrigo is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $5,300 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this nonpayment period, interest will accrue at 4.29%.

a. How much interest will Rodrigo accrue during the 4.5-year nonpayment period?

b. If Rodrigo decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. What will the new principal be when he begins making loan payments, and how much interest will he pay over the life of the loan?

c. Suppose Rodrigo only paid the interest during his 4 years in school and the 6-month grace period. What will he now pay in interest over the term of his loan?

d. Rodrigo made his last monthly interest-only payment on July 8. His next payment is due on August 8. What will be the amount of that interest-only payment?

9. Maribel was approved for a 7-year private student loan at 6.8% to cover her college costs of $10,900.

a. Determine her monthly payment. Round to the nearest cent. b. What is the total amount she will pay back? c. What is the total interest amount?

$281.38

$218.25$1,454.04

$1,672.29$217.29

$0

391%

$204.03$7,345.08

$345.08

$1,500.00

$870

$1,023.17

$6,323.17; $2,486.80

$2,249.97

$19.31

$163.45$13,729.80

$2,829.80

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10. Ben has been accepted into a 2-year culinary arts program at the Greenfield Career Institute. He has been approved for a $5,000 unsubsidized 10-year federal loan at 4.29%. He knows he has the option of beginning repayment of the loan in 2.5 years. He also knows that during this nonpayment period, interest will accrue at 4.29%.

a. How much interest will Ben accrue during the 2.5-year nonpayment period?

b. If Ben decides to make no payments during the 2.5 years, the interest will be capitalized at the end of that period. What will the new principal be when he begins making loan payments, and how much will he pay in interest over the life of the loan?

c. Suppose Ben only paid the interest during his 2 years in school and the 6-month grace period. What will he pay in interest over the term of his loan?

d. Ben made his last monthly interest-only payment on September 25. His next payment is due on October 25. What will be the amount of that interest-only payment?

11. Juan purchased a tool set for t dollars on the installment plan. He made a 15% down payment and agreed to pay m dollars per month for the next y years. Express the finance charge algebraically.

12. Blair had these daily balances on his credit card for his last billing period. He did not pay the card in full the previous month, so he will have to pay a finance charge. The APR is 18.6%.2 days @ $331.9811 days @ $1,203.044 days @ $996.7113 days @ $1,002.76

a. What is the average daily balance? Round to the nearest cent. b. What is the finance charge?

13. Kim’s credit card was not paid in full last month so she will pay a finance charge this month. She had an average daily balance of d dollars during this billing period, which had 31 days. The APR was p percent.

a. Express the APR as an equivalent decimal algebraically. b. Express the monthly percentage rate as an equivalent decimal algebraically. c. Express the finance charge algebraically.

14. Michelle’s credit card billing cycle is 30 days. She had a daily balance of b dollars for d days. Then she charged one item for $56, and she made no more purchases for the rest of the month. There was no other activity on the credit card. Express her average daily balance algebraically.

15. The finance charge on Lena’s credit card bill last month was $13.50. Her APR is 18%. What was her average daily balance?

16. Riel had an average daily balance of $415.22 on his May credit card statement. The bill showed that his APR was 21.6% and that his finance charge was $89.69. When he verified the finance charge, did he find that it was correct or incorrect? Explain.

17. What is the monthly periodic rate on a loan with an APR of 19.5%?18. Harold borrowed $8,000 for 5 years at an APR of 2.75%.

a. What is Harold’s monthly payment? Round to the nearest cent. b. What is the total amount that Harold paid in monthly payments for the

loan? c. What is the amount Harold will pay in finance charges?

ANSWERS16. Incorrect; the APR should

be divided by 12 before multiplying by the average daily balance. The correct finance charge is $7.47.

$536.25

$5,536.25; $1,818.40

$1,157.20

$17.63

0.15t +12ym 2 t 5 12ym 2 0.85t

$1,030.67$15.98

0.01p

$900

See margin.

1.625%

$142.86

$8,571.60$571.60

p

0.0112p

d

0.0112

bd d b+ +(30 – )( 56)30

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Assessment 207

19. Examine the summary section of the monthly credit card statement. Use the first five entries to determine the new balance.

PreviousSUMMARY

$421.36


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$1,703.50 $1,273.11 $0.00 $9.03 $18.00

NewPurchases

Year Balance

0 $50,000.00

1 $48,201.08

2 $46,252.85

3 $44,142.91

4 $41,857.85

5 $39,383.13

6 $36,703.01

7 $33,800.44

8 $30,656.96

9 $27,252.57

10 $23,565.62

11 $19,572.66

12 $15,248.28

13 $10,564.98

14 $5,492.97

15 $0.00

PreviousSUMMARY

$978.00


LateCharge

FinanceCharge

NewBalance

MinimumPayment

�$1,340.00 $2,057.65 $115.00

TRANSACTIONS

7 APR 124576893

15 APR 762938471


$676.00

$93.1519 APR 309175832

2$1,340.00

AverageDaily


MonthlyPeriodic

Balance Cycle Rate

30 19.8% 1.65%

ACCOUNT INFORMATION

Account Number 3-22767195 Billing Date 5 May Payment Due 18 May


$ 3,000.00

27 APR

30 APR

100445638

876655411

$721.80

$115.75

$0.00

3 MAY 998430828

Macy’s

Bedford Auto Body Shop

Barnes and Noble Books

Payment

FedEx

TicketMaster $450.95

NewPurchases

20. The table lists the balances at the end of each year for a 15-year, $50,000 loan with an 8% interest rate.

a. Construct a scatter plot using the data points (year, loan balance).

b. Write a linear regression equation that approximates the year–loan balance relationship. Round to the nearest integer.

c. Write a quadratic regression equation that approximates the year–loan balance relationship. Round to the nearest integer.

d. Write a cubic regression equation that approximates the year–loan balance relationship. Round to the nearest integer.

21. Bill can afford a monthly payment of $475. He wants to take out a $20,000 loan at a 4.25% interest rate. What should the length of the loan be? Round your answer to the nearest year.

22. Kayla wants to take out a $7,500 loan with a 3.3% APR. She can afford to pay $128 per month for loan payments.

a. What should be the length of her loan? Round to the nearest tenth of a year.

b. What would an increase of $20 to the monthly payment do to the length of her loan?

23. Use the credit card statement and a blank credit card calendar.

a. What is the total of all of the purchases made this billing cycle? b. What is the amount of total payments? c. What is sum of the daily balances? d. What is the average daily balance? Round to the nearest cent. e. What is the monthly periodic rate? f. What is the finance charge? Round to the nearest cent. g. What is the new balance? h. What is the available credit?

y = 23,271x 1 54,077

y = 2129x2 2 1,338x 1 49,566

y = 23x3 2 52x2 2 1,782x 1 50,030

ANSWERS20a.

See margin.

approx. 4 years

5.3 years

It would decrease the loan length to 4.6 years.

$2,057.65$1340.00

$55,672.70$1,855.76

1.65%$30.62

$1,726.27$1,273.73

The answer to Q9 is $0

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Chapter 3 Consumer Credit - Cengage · PDF fileChapter 3 Consumer Credit ... think of loans...

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Transcript of Chapter 3 Consumer Credit - Cengage · PDF fileChapter 3 Consumer Credit ... think of loans...