Question

The repayment schedule is for a $1,300 loan at 7.5% for 6 months. What is the amount for interest at payment 5?

Answer 1

$2.77

Explanation:

Here's one way to do it.

Data:

We must express the interest rate on a monthly basis.

i = 7.5 %/yr = 0.625 %/mo = 0.006 25

A = $1300

n = 6 mo

A. Monthly payments

The formula for the monthly payment (P) on a loan of A dollars that is paid back in equal monthly payments over n months, at an annual interest rate of i % is

`P = A((i)/(1-(1+i)^(-n)))`

Calculation:

`P = 1300((0.006 25)/(1-(1+0.006 25)^(-6)))`

`P = \frac{8.125}{{1- {1.006 25}}^(-6)}`

`P = (8.125)/(1 - 0.9633)`

`P = (8.125)/(0.03669)`

P = $221.43

B. Total amount paid over six months

Paid = 6 × 221.43

Paid = $1328.58

C. Amount paid after four months

Paid = 4 × 221.43

Paid = $885.72

D. Balance owed after four months

Owed = 1328.58 - 885.72

Owed = 1341.14 – 1121.08

Owed = $442.86

E. Interest included in Payment 5

I = Pi

I = 442.86 × 0.006 25

I = $2.77

The interest included in Payment 5 is $2.77.