McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, All Rights Reserved

Chapter 10

Simple InterestSimple Interest

10-2

1. Calculate simple interest and maturity value for months and years

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

Simple Interest#10#10Learning Unit ObjectivesCalculation of Simple Interest and Maturity Value

LU10.1LU10.1

10-3

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

Simple Interest#10#10Learning Unit ObjectivesFinding Unknown in Simple Interest Formula

LU10.2LU10.2

10-4

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

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

Simple Interest#10#10Learning Unit ObjectivesU.S. Rule -- Making Partial Note Payments before Due Date

LU10.3LU10.3

10-5

Maturity Value

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

The amount of the loan(Face value)

Cost of borrowing

money

10-6

Simple Interest Formula

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

Stated as aPercent Stated in

years

Jan Carley borrowed $30,000 for office furniture. The loan was for 6 months at an annual interest rate of 8%. What are Jan’s interest and maturity value?

SI = $30,000 x.08 x 6 = $1,200 12

MV = $30,000 + $1,200 = $31,200

10-7

Simple Interest Formula

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

Stated as aPercent Stated in

years

Jan borrowed $30,000. The loan was for 1 year at a rate of 8%. What is interest and maturity value?

SI = $30,000 x.08 x 1 = $2,400MV = $30,000 + $2,400 = $32,400

10-8

Two Methods of Calculating Simple Interest and Maturity Value

Exact Interest (365 Days)

Time = Exact number of days 365

Method 1 – Exact InterestUsed by Federal Reserve banksand the federal government

I = P X R X T$40,000 x .08 x 124 365$1,087.12MV = P + I$40,000 + $1,087.12$41,087.12

Exact Interest (365 Days)

On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.

10-9

Two Methods of Calculating Simple Interest and Maturity Value

Ordinary Interest (360 Days)

Bankers Rule

Time = Exact number of days 360

I = P X R X T$40,000 x .08 x 124 360$1,102.22MV = P + I$40,000 + $1102.22$41,102.22

Ordinary Interest (360 Days)

On March 4, Peg Carry borrowed $40,000 at 8%. Interest and principal are due on July 6.

Method 2 – Ordinary InterestBankers Rule

10-10

Two Methods of Calculating Simple Interest and Maturity Value

Exact Interest (365 Days)

I = P X R X T$15,000 x .08 x 98 365$322.19MV = P + I$15,000 + $322.19$15,322.19

Ordinary Interest (360 Days)

On May 4, Dawn Kristal borrowed $15,000 at 8%. Interest and principal are due on August 10.

I = P X R X T$15,000 x .08 x 98 360$326.67MV = P + I$15,000 + $326.67$15,326.67

10-11

Finding Unknown in Simple Interest Formula - PRINCIPAL

Principal = Interest Rate x Time

Tim Jarvis paid the bank $19.48 interest at 9.5% for 90 days. How much did Timborrow using ordinary interest method?

$19.48 .P = .095 x (90/360) = $820.21

.095 times 90 divided by 360. Do not round answer

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

Check: 19.48 = 820.21 x .095 x 90/360

10-12

Finding Unknown in Simple Interest Formula - RATE

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

Check: 19.48 = 820.21 x .095 x 90/360

Rate = Interest Principal x Time

Tim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using ordinary interest method?

$19.48 .R = $820.21 x (90/360) = 9.5%

10-13

Finding Unknown in Simple Interest Formula - TIME

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

Check: 19.48 = 820.21 x .095 x 90/360

Time (yrs) = Interest Principle x Rate

Tim Jarvis borrowed $820.21 from a bank. Tim’s interest is $19.48 for 90 days. What rate of interest did Tim pay using ordinary interest method?

$19.48 .T = $820.21 x .095 = .25

.25 x 360 = 90 days

Convert years to days (assume 360 days)

10-14

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

10-15

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

Joe Mill owes $5,000 on an 11%, 90-day note. On day 50, Joe pays $600 on the note. On day 80, Joe makes an $800 additional payment. Assume a 360-

day year. What is Joe’s adjusted balance after day 50 and after day 80? What is the ending balance due?

$5,000 x .11 x 50 = $76.39 360

$600 - 76.39 = $523.61$5,000 – 523.61 = $4,476.39

10-16

U.S. Rule - Example

Step 3. Calculate interest on adjusted balance that starts from previous payment date and goes to new payment date. Then

apply Step 2.

Step 4. At maturity, calculate interest from last partial payment. Add this

interest to adjusted balance.

Joe Mill owes $5,000 on an 11%, 90-day note. On day 50, Joe pays $600 on the note. On day 80, Joe makes an $800 additional payment. Assume a 360-

day year. What is Joe’s adjusted balance after day 50 and after day 80? What is the ending balance due?

$4,476.39 x .11 x 30 = $41.03360

$800 - 41.03 = $758.97$4,476.39 – 758.97 = $3717.42

$3,717.42 x .11 x 10 = $11.36 360

$3,717.42 + $11.36 = $3,728.78