Seminar 6Chapters 8 and 9

Unit 6

Key Terms• Interest: an amount paid or earned for the use

of money.• Simple interest: interest earned when a loan or

investment is repaid in a lump sum.• Principal: the amount of money borrowed or

invested.• Rate: the percent of the principal paid as interest

per time period.• Time: the number of days, months or years that

the money is borrowed or invested.

The Simple Interest Formula

• The interest formula shows how interest, rate, and time are related and gives us a way of finding one of these values if the other three values are known.

I = P x R x T

Find the simple interest using the simple interest formula

Identify the principal, rate and time

P = R x B

• The interest is a percentage.

• Principal is the amount borrowed or invested.

• Rate of interest is a percent for a given time period, usually one year.

• Time must be expressed in the same unit of time as the rate. (i.e. one year)

Find the interest paid on a loan

• Principal = (P) $1,200

• Interest rate = 8% (or 0.08)

• Time = 1 year

• Interest = P x R x T

• Interest = 1,200 x 0.08 x 1

• Interest = $96

• The interest on the loan is $96

Convert Months to a Fractional or Decimal Part of a Year

• Write the number of months as the numerator of a fraction.

• Write 12 as the denominator of the fraction.

• Reduce the fraction to lowest terms if using the fractional equivalent.

• Divide the numerator by the denominator to get the decimal equivalent of the fraction

Convert the following to fractional or decimal part of a year

• Convert 9 months and 15 months, respectively, to years, expressing both as fractions and decimals.

• 9/12 = ¾ = 0.75

• 9 months = ¾ or 0.75 of a year

• 15/12 = 1 3/12 = 1 ¼ = 1.25

• 15 months = 1 ¼ or 1.25 of a year.

Look at this example• To save money, Stan Wright invested $2,500 for

42 months at 4 ½ % simple interest. How much interest did he earn?

• 42 months = 42/12 = 3.5• I = P x R x T• I = $2,500 x 0.045 x 3.5• I = $393.75• Stan will earn $393.75

Find the Principal, Rate or Time Using the Simple Interest Formula

Ordinary and Exact Interest

Find exact time .

Find the due date.

Find the ordinary interest and the exact interest.

Make a partial payment before the maturity date.

Find Exact Time

• Ordinary time: time that is based on counting 30 days in each month.

• Exact time: time that is based on counting the exact number of days in a time period.

Examples• The ordinary time from July 12 to September 12 is 60 days.

• To find the exact time from July 12 to September 12, add the following:

Days in July (31 - 12 =) 19

Days in August 31

Days in September +12

62 days

Sequential Numbers for Dates of the Year

• Find the exact time of a loan using the sequential numbers table. (Table 11-1 in the text)

• If the beginning and due dates of the loan fall within the same year, subtract the beginning date’s sequential number from the due date’s sequential number.

• Ex.: From May 15 to October 15

• 288-135 = 153 days is the exact time

Beginning and due dates in different years

• Subtract the beginning date’s sequential number from 365.

• Add the due date’s sequential number to the result from the previous step.

• If February 29 falls between the two dates, add 1. (Is it a leap year?)

Look at this example

• Find the exact time from May 15 on Year 1 to March 15 in Year 2.

• 365 – 135 = 230

• 230 + 74 = 304 days

• The exact time is 304 days.

• Note: If Year 2 is a leap year, the exact time is 305 days.

Try this example

• A loan made on September 5 is due July 5 of the following year.

• Find: a) ordinary time b) exact time in a non-leap year c) exact time in a leap year.

• Ordinary time = 300 days

• Exact time (non-leap year) = 303 days

• Exact time (leap year) = 304 days

Find the Ordinary Interest and the Exact Interest

• Ordinary interest: a rate per day that assumes 360 days per year.

• Exact interest: a rate per day that assumes 365 days per year.

• Banker’s rule: calculating interest on a loan based on ordinary interest and exact time which yields a slightly higher amount of interest.

Find the ordinary interest per day

• For ordinary interest rate per day, divide the annual interest rate by 360.

Ordinary interest rate per day =

Interest rate per year360

Use ordinary time to find the ordinary interest on a loan

• A loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500) I = P x R x T

• Length of loan (ordinary time) = 60 days

• Rate = 0.07/360 (ordinary interest)

• Interest = $500 x 0.07/360 x 60

• Interest = $5.83

Find the ordinary interest using exact time for the previous loan

• A loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500) I = P x R x T

• Length of loan (exact time) = 61 days

• Rate = 0.07/360 (ordinary interest)

• Interest = $500 x 0.07/360 x 61

• Interest = $5.93

Find the exact interest using exact time for the previous loan

• A loan of $500 at 7% annual interest rate. The loan was made on March 15 and due on May 15. (Principal = $500) I = P x R x T

• Length of loan (exact time) = 61 days

• Rate = 0.07/365 (exact interest)

• Interest = $500 x 0.07/365 x 61

• Interest = $5.84

Chapter 9Consumer Credit

Key Terms

• Consumer credit: a type of credit or loan that is available to individuals or businesses. The loan is repaid in regular payments.

• Installment loan: a loan that is repaid in regular payments.

• Closed-end credit: a type of installment loan in which the amount borrowed and the interest is repaid in a specific number of equal payments.

Key Terms

• Open-end credit: a type of installment loan in which there is no fixed amount borrowed or number of payments. Regular payments are made until the loan is paid off.

• Finance charges or carrying charges: the interest and any fee associated with an installment loan.

Find the Amount Financed, the Installment Price and the Finance

Charge of an Installment Loan• Cash price: paid all at once at time of

purchase

• Down payment: partial payment

• Amount financed: total amount paid in regular payments to pay off the balance

• Installment price: includes all installment payments, finance charges and down payment

Look at this example

• The 7th Inning purchased a mat cutter for the framing department on the installment plan with a $60 down payment and 12 payments of $45.58. Find the installment price of the mat cutter.

• Installment Price (IP) = total of installment payments + down payment

• IP = (12 x $45.58) + $60• IP = $546.96 + 60 = $606.96

Try this example

• Peggy bought a new dryer on an installment plan. She made a down payment of $100. The installment price for a five month loan was $412.50. What was the installment payment?

Answer

• $412.50 (100.00) down payment $312.50 financed for 5 months Payments = $62.50

Find the Estimated APR Using a Table

Annual percentage rate (APR): the true rate of an installment loan that is equivalent to an annual simple interest rate.

Truth in Lending Act: passed in 1969 by the federal government, it requires a lending institution to tell the borrower in writing what the APR actually is.

Annual Simple Interest Rate Equivalent

• Example: If you borrowed $1,500 for one year and were charged $165 in interest, you would be paying an interest rate of 11% annually.

• $165 ÷ $1,500 = 0.11 = 11%

• If you paid the money back in 12 monthly installments of $138.75, you would not have use of the entire $1,500 for a full year.

• In effect you would be paying more than the 11% annually.

Percentage rate tables

• The APR can be determined using a government-issued table.

• APR rates are within ¼ % which is the federal standard.

• A portion of one of these tables based on the number of monthly payments is shown in your text in Table 9-1

Using a per $100 of amount financed table

Find the interest per $100 financed; divide the finance charges including interest by the amount financed and multiply by $100.

2. Find the row corresponding to number of monthly payments. Move across the row to find the number closest to the value from step 1. Read up the column to find the APR for that column.

Look at this example

Lewis Strang bought a motorcycle for $3,000, which was financed at $142 per month for 24 months. There was no down payment.

Find the APR.

Installment price = $142 x 24 = $3,408

Finance charge = $3,408 - $3,000 = $408

Find the APR using the table

• Interest per $100 = finance charge x $100 = amount financed

• $408 $3,408 x $100 = $11.97

• Find the row for 24 monthly payments.• Move across to find the number nearest to

$11.97.• Move up to the top of that column to find the

APR which is 11%

Try this example

• Find the APR for Jody’s new laptop which cost $1,800 and was financed for 12 months. There was no down payment. The monthly payments were $168.

• Answer: • Installment price = $168 x 12 = $2,016• Finance charge = $2,016 - $1,800 = $216• $216/$2016 = 0.10714 x100 = $10.71• The APR is 19.25%

Paying a Loan Before it is Due

• If a loan is paid before it is due, some of the interest may be refunded.

• It may be less than what you expected.

• Find the interest refund using the rule of 78:

A method for the amount of refund of finance charge for an installment loan that is paid before it is due.

How to find the refund fraction

In a twelve-month loan:• Month 1: Interest accrues on 12 parts of the

principal.• Month 2: Interest accrues on 11 part of the

principal• Month 3: Interest accrues on 10 parts of the

loan and so on.• At the end of 12 months, there is a total of 78

parts: 12 + 11 +10 + 9 + 8 + 7… + 1 = 78

the loan is paid off at the end of month 9

• Month 10: interest is accrued on 3 parts of the principal.

• Month 11: interest is accrued on 2 parts of the principal.

• Month 12: interest is accrued on 1 part of the principal.

• The sum is 3 + 2 + 1 = 6

• Therefore, 6/78 of the total interest must be refunded.

Look at this example

A loan for 12 months with interest of $468.85 is paid in full with five payments remaining. What is the refund fraction for the interest refund?

5 + 4 + 3 + 2 + 1 = 15 (parts) remaining out of 78

15/78 would be applied to the interest to calculate the interest refund.

Open-End Credit

• Find the finance charge and the new balance using the average daily balance method.

Open-End Credit

• Also known as “line of credit” accounts.

• Adding to an existing loan happens when a person or company,– Makes additional purchases before paying off

existing debt.– Makes the minimum payment, adding to finance

charges– Takes cash advances, incurring interest charges– Adds additional debit obligations

When does the balance change?

• In most cases, if a transaction reaches a financial institution at any time during the day, the transaction is posted and the balance is updated at the end of the business day.

• Calculations on the day’s unpaid balance are made on the end-of-day amount (same as the beginning of the next day.)

Find the Average Daily Balance

Daily unpaid balance = previous daily unpaid balance + total purchases and cash advances for the day– total credits for the day.

Average daily balance = Sum of unpaid balances

Number of days in a billing cycle

Look at this example

Hodge’s Tax Service

Hodge’s Tax Service

TIP!!

The unpaid balance on an account for a billing cycle is the unpaid daily balance for the last day of the billing cycle.

The beginning balance for the next cycle is the unpaid balance for the previous cycle.

• Any Questions????