1-1 1-2 Chapter 10 Simple Interest McGraw-Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies,...

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Chapter 10Chapter 10

Simple InterestSimple Interest

McGraw-Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.

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• Calculate simple interest and maturity value for months and years

• Calculate simple interest and maturity value by (a) exact interest and (b) ordinary interest

Simple Interest#10#10Learning Unit Objectives

Calculation of Simple Interest and Maturity Value

LU10.1LU10.1

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Maturity Value

Maturity Value (MV) = Principal (P) + Interest (I)

The amount of the loan(Face value)

Cost of borrowing

money

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Simple Interest Formula

Simple Interest (I) = Principal (P) x Rate (R) x Time (T)

Stated as aPercent

Stated in years

Ryan borrowed $20,000. The loan was for 6 months at a rate of 9%. What is interest and maturity value?

SI = $20,000 x.09 x 6 = $900 12

MV = $20,000 + $900 = $20,900

Beg. amountborrowed

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Calculate Simple Interest

• LoanStar bank is offering a $10,000 year loan with 7.5% interest. How much will the interest be at the end of the year?

• I = P X R X T• I = 10,000 x .075 x 1 = $750• What is the Maturity value at the end of the year?• MV = P + I• MV = 10,000 = 750 = 10,750

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Calculate Simple Interest

• LoanStar bank is offering a $4,000 monthly loan with 8% interest. How much will the interest be at the end of the 4 months?

• I = P X R X T• I = 4,000 x .08 x 4/12 = $106.67• What is the Maturity value at the end of the year?• MV = P + I• MV = 4,000 + 106.67 = 4106.67• How much interest will there be after two years?• I = 4,000 x .08 x 2 = 640

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Two Methods of Calculating Simple Interest and Maturity Value

Exact Interest (365 Days)

Time = Exact number of days 365

Ordinary Interest (360 Days)

Bankers Rule

Time = Exact number of days 360

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Simple Interest—Exact

• Using Exact Interest:• I = P x R x T (days/365)

• A loan is taken for $20,000, payable in 90 days at a rate of 9%. What is the interest and maturity value?

• I = 20,000 x .09 x 90/365• I = 443.84• MV = 20,443.84

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Simple Interest--Ordinary

• Using Ordinary Interest:• I = P x R x T (days/360)

• A loan is taken for $25,000, payable in 90 days at a rate of 9%. What is the interest and maturity value?

• I = 25,000 x .09 x 90/360• I = 562.5• MV = 25,562.50

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Calculate using Exact Interest

• John goes to WeTrustEm Bank to get a loan to buy a car. He needs to borrow $7,500. He will be receiving his tax refund in 60 days, so the bank offers him a loan for 6% for the 60 days. The bank uses exact interest.

• What is the total amount John must pay back to the bank after 60 days?

• 7500 x .06x 60/365 = 73.97 + 7500 = 7573.97

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Calculate using Ordinary Interest

• John decided he cannot afford the $7500 loan. He found a different car for $5450. He goes to MoneyLenders to get a loan, and agrees to a 90 day period at 6.5%, with ordinary interest calculated.

• What must John repay for this loan?• 5450 * .065 * 90/360 = 88.56 + 5450 = 5538.56

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Finding Days in a Loan Period

• Calendar Method—Exact days (365 days)• Count the days between the beginning of the loan, and the

payment date• Don’t count the initial day of the period

• Table method—Exact days• Find the number of the beginning day• Add the number of days in the period to this• Find this numbered day as your due date

• Ordinary Interest—360 days• Assume each month has 30 days

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Finding Days in a Loan Period

• A note made on Sept. 15 was repaid on Nov. 30; use the calendar method. How many days?• Sept 15 to Sept 30 = 30 – 15 = 15• Oct. 1 to Oct 31 = 31• Nov 1 to Nov 30 = 30• Total = 76 days

• A note made on Sept 20 was repaid on March 15; use the table• Sept 20 = 263; Dec 31 = 365; 365 – 263 = 102• To March 15—day 74; 102 + 74 = 176

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Finding the Due Date of a Loan

• A 60-day note was signed on Sept. 20. When is the due date of the loan, using the calendar method.• Sept 20—30 = 10• Oct 31 41 days• Nov 19

60

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• A 60-day note was signed on Sept. 20. When is the due date of the loan, using the table method.• Sept 20 = day 263• Add days +60• Due day number 323 • Nov. 19

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• A note due in 120 days was made on Oct. 18. Use the table method to find the date the note is due.• Oct 18 = 291• Dec 31 = 365• days 74• 120 – 74 = 46 days remaining• 46 = Feb 15

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Assignment

• Review pps. 243—246• Work Drill problems #10-1 to 10-9, p. 253

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Review—finding due date

• A 120 day note was made on June 23. What is the due date of this note?

• June 23 = 174• + 120• 294 = Oct. 21

• A 90 day note is due on Feb. 27. On what date was this note made?

• Feb 27 = 58• -90• 32 back in previous year• 365 – 32 = 333 = Nov. 29

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Review—finding Maturity of a Note

• Sara borrowed $2500 today from Good Deal Credit Union. She promised to pay it back in full by the end of the year, with 8% interest. How much must Sara pay on Dec. 31 ?

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• Using the interest formula, calculate the unknown when the other two (principal, rate, or time) are given


Finding Unknowns in Simple Interest Formula

LU10.2LU10.2

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Using the Formula--Interest

I = P x R x TWe will assume Ordinary Interest

IP x R x T

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Using the Formula--Principle

P = I / (R * T)

IP x R x T

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Using the Formula--Rate

R = I / (P * T)

IP x R x T

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Using the Formula--Time

T = I / (P * R)

IP x R x T

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Finding Unknown in Simple Interest Formula - Principal

Principal = Interest Rate x Time

Interest (I) = Principal (P) x Rate (R) x Time (T)

Christina Jones paid the bank $44 interest at 11% for 120 days. How much did she

borrow?

$44 .P = .11 x (120/360)

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borrow?

$44 . 4 P = .036666667

.11 times 120 divided by 360. Do not round answer

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borrow?

$44 .P = .11 x (120/360) = $1,200

.11 times 120 divided by 360. Do not round answer

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Finding Unknown in Simple Interest Formula - Rate

Rate = Interest Principal x Time


Christina Jones borrowed $1,200 from the bank. Her interest

is $44 for 120 days. What rate of interest did Christina pay?

$44 .R = $1,200 x (120/360) =

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Finding Unknown in Simple Interest Formula - Rate

Rate = Interest Principal x Time


Christina Jones borrowed $1,200 from the bank. Her interest

is $44 for 120 days. What rate of interest did Christina pay?

$44 .R = 400 = .11

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Finding Unknown in Simple Interest Formula - Time

Time = Interest Principle x Rate


$44 .T = $1,200 x .11

Christina Jones borrowed $1,200 from the bank. Her interest is $44 for 11%. How

much time does Christina have to repay the loan?

$44 .T = 132

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Finding Unknown in Simple Interest Formula - Time

Time = Interest Principle x Rate


$44 .T = $1,200 x .11 = .33

Christina Jones borrowed $1,200 from the bank. Her interest is $44 for 11%. How

much time does Christina have to repay the loan?

Convert years to days (assume 360 days).33 x 360 = 120 days

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Use the Interest Formula

• A loan for $157,000 was charged 10.75% interest. The interest amounted to $6,797.88. What amount of time was this loan for?

• T = I/P*R• T =6797.88 / (.1075* 157000)• T = 6797.88 / 16877.5• T = .40278• T= .40278 * 360 = 145 days

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• A loan for $7,500 charged interest of $350. The loan was paid in 120 days. What interest rate was charged?

• R = I / P * T• R = 350 / (7500*120/360)• R = 350 / 2500• R = .14 = 14%

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• A loan for 120 days with 9% interest shows a total interest due of $103. What was the original amount of the loan?

• P=I/R*T• P = 103 / (.09 * 120/360)• P = 103 / .03• P = $3433.33

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Assignment

• review pps. 246—248• work drill problems 10-10 to 10-12, p. 254

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Interest Formula—review 1

• A loan for $55,000 charged interest of $1,100. The loan was paid in 90 days. What interest rate was charged?

• R = I / P * T• R = 1100 / (55000*90/360)• R = .08 = 8%

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• A loan for $50,000 was charged 7.75% interest. The interest amounted to $1453.13. What amount of time was this loan for?

• T = I/P*R• T =1453.13 / (.0775* 50000)• T = 1453.13 / 3875• T = .375• T= .375 * 360 = 135 days

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• A loan for 2 years with 9% interest shows a total interest due of $459. What was the original amount of the loan?

• P=I/R*T• P = 459 / (.09 * 2)• P = 459 / .18• P = $2550

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• A loan for $45,000 at 6.5% was made on Nov. 15. The loan was repaid on March 31. What was the amount of interest on the loan using exact interest? What was the maturity value?

• I = P x R x T• I = 45000 x .065 x 136/365• I = 1089.86• MV = 46089.86

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• List the steps to complete the U.S. Rule

• Complete the proper interest credits under the U.S. Rule


U.S. Rule -- Making Partial Note Payments before Due Date

LU10.3LU10.3

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U.S. Rule - Making Partial Note Payments before Due Date

Any partial loan payment first covers any interest that has built up. The remainder of the partial payment

reduces the loan principal.

Allows the borrower to receive proper interest credits

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Using the U.S. Rule

Step 1. Calculate interest on principal from date of loan to date of first principal payment

Step 2. Apply partial payment to interest due. Subtract remainder of payment from principal

Step 3. At maturity, calculate interest from last partial payment. Add this interest to adjusted balance.

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U.S. Rule - Example

Step 1. Calculate interest on principal from date of loan to date of first principal

payment

Step 2. Apply partial payment to interest due. Subtract remainder of payment from

principal

Step 3. At maturity, calculate interest from last partial payment. Add this

interest to adjusted balance.

Darren owes $3,000 on an 10%, 90 day note. On day 40, Darren pays $1,200 on the note. Assume a 360- day year. What is Darren’s Adjusted balance

after day 40? What is the ending balance due?

$3,000 x .10 x 40 = $33.33 360

$1,200 - 33.33 = $1,166.67$3,000 - 1,166.67 = $1,833.33

$1,833.33 x .10 x 50 = $25.46 360

$25.46 + $1,833.33 = $1,858.79

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Use the U.S. Rule

• Jesse borrowed $10,800 on a 1-year note at 14%. After 60 days, Jesse received a tax refund and paid $2,500 on the note. On her birthday, day 200 of the loan, Jesse received a $5,000 check from her Grandmother, and she applied it toward her loan. What will be the total interest and final balance due on the loan?

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• Jesse borrowed $10,800 on a 1-year note at 14%. After 60 days, Jesse received a tax refund and paid $2,500 on the note. On her birthday, day 200 of the loan, Jesse received a $5,000 check from her Grandmother, and she applied it toward her loan. What will be the total interest and final balance due on the loan?

• Step 1. 10,800 x .14 x 60/360 = 252• Step 2. 2500 – 252 = 2248 (applied against principle)• 10,800 – 2248 = 8552 (new principle balance)• Find number of days in second period• 200 – 60 = 140• repeat step 1 & 2 for second payment• 8552 x .14 x 140/360 = 465.61• 5000 – 465.61 = 4534.39 (applied against principle)• 8552 – 4534.39 = 4017.61 (new principle balance)• Step 3. find days remaining: 360 – 200 = 160• 4017.61 x .14 x 160/360 = 249.98• Final balance due: 4017.61 + 249.98 = 4,267.59• Total interest cost: 252.00 + 465.61 + 249.98 = 967.59

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#10-13• 10000 x .08 x 100/360 = 222.22 interest• 4000 – 222.22 = 3777.78 apply to principal• 10000 – 3777.78 = 6222.22 adjusted balance• 6222.22 x .08 x 80/360 = 110.62 interest• 2000 – 110.62 = 1889.38 to principal• 6222.22 – 1889.38 = 4332.84 new balance• 4332.84 x .08 x 60/360 = 57.77 interest• 4332.84 + 57.77 = 4390.61 balance due• 222.22 + 110.60 + 57.77 = 390.61 total interest

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Assignment

• Review pps. 249—251• work Drill problem 10-13, p. 254• do Word Problems #14--23

1-1 1-2 Chapter 10 Simple Interest McGraw-Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies,...

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