Answer to Question #200089 in Financial Math for Cynthia Letlatla

Question

You buy a computer directly from the manufacturer for R7332,00 and agree to repay it in equal instalments over three years at the end of each month, starting one month from now. The interest rate is 10,7% per year, compounded monthly. How much interest will you pay in total?

Answer 1

Given the following:

Future value (FV)= R7332

Rate (r)= 10.7% or 0.107

Time (n)= 3 years

The installment parent is given by

$PV=\frac{FV}{[\frac{(1+r)^n-1}{r}]}$

$PV=\frac{7332}{[\frac{(1+0.107)^3-1}{0.107}]}$

$PV=R2200.18$

The picture above shows the payment schedule.

In the 2nd year, on R2200.18 balance @10.7%, the interest would be 235.42

Hence the balance to be paid in 2nd year would be

(2200.18 + 2200.18 + 235.42) = R4635.7

In the 3rd year, on R4635.7 balance @10.7%, the interest would be 496.02

Hence the balance to be paid in 3rd year would be

(4635.7 + 2200.18 + 496.02) = R7331.9

The total interest due in the payment according to the table will be

(235.42+496.02) = R731.44