Chapter TenSIMPLE INTEREST

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10-2

LEARNING UNIT OBJECTIVES

LU 10-1: Calculation of Simple Interest and Maturity Value

1. List the steps to complete the U.S. Rule.2. Complete the proper interest credits under the U.S. Rule.

LU 10-3: U.S. Rule -- Making Partial Note Payments before Due Date

LU 10-2: Finding Unknown in Simple Interest Formula

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

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.

10-3

MATURITY VALUE

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

The amount of the loan(face value)

Cost of borrowing

money

10-4

SIMPLE INTEREST FORMULA

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

Stated as aPercent

Stated in Years

Example: 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?

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

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

10-5

SIMPLE INTEREST FORMULA

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

Stated as aPercent

Stated in years

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

I = $30,000 x .08 x 1 = $2,400 interest

MV = $30,000 + $2,400 = $32,400 maturity value

10-6

TWO METHODS OF CALCULATING SIMPLE INTEREST AND MATURITY

VALUE

Exact Interest (365 Days)

Time = Exact number of days 365

Method 1: Exact Interest Used by Federal Reserve banks and the federal government

10-7

METHOD 1:EXACT INTEREST

Exact Interest (365 Days)

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

I = P x R x T 124 365$40,000 x .08 x

= $1,087.12 interest

MV = P + I$40,000 + $1,087.12 = $41,087.12 maturity value

10-8

TWO METHODS OF CALCULATING SIMPLE INTEREST AND MATURITY

VALUE

Ordinary Interest (360 Days)

Time = Exact number of days 360

Method 2 : Ordinary Interest (Banker’s Rule)

10-9

METHOD 2ORDINARY INTEREST

Ordinary Interest (360 Days)

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

MV = P + I$40,000 + $1102.22 = $41,102.22 maturity value

I = P x R x T 124 360$40,000 x .08 x

= $1,002.22 interest

10-10

TWO METHODS OF CALCULATING SIMPLE INTEREST AND MATURITY

VALUE

Exact Interest (365 Days)

MV = P + I$15,000 + $322.19 = $15,322.19

Ordinary Interest (360 Days)

MV = P + I$15,000 + $326.67 = $15,326.67

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

I = P X R X T 98 365

$15,000 x .08 x

= $322.19 interest

I = P X R X T 98 360

$15,000 x .08 x

= $326.67 interest

10-11

FINDING UNKNOWN IN SIMPLE INTEREST FORMULA: PRINCIPAL

Principal = Interest Rate x Time

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

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

.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

Example: 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 the 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 (years) = Interest Principle x Rate

Example: 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?

T = $19.48

= .25. $820.21 x .095 .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.

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U.S. RULE(EXAMPLE)

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

principalpayment.

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?

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

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

10-16

U.S. RULE(EXAMPLE, CONTINUED)

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 = $41.03 360

$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