Answer to Question #219162 in Financial Math for ZM MJOMENI

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 form 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 installmental 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.

From the table to get interest for Year 2 $=$ 2200.18$($ PV of year 1$)$ $×$ 10.7%$=$ 235.42

Balance to be paid$=$ annual installment$+$ deposit$+$ interest

2200.18$+$ 2200.18$+$ 235.42$=$ 4635.7

Interest for year 3$=$ 4635.7$×$ 10.7%$=$ 496.02

Balance to be paid$=$ 2200.18$+$ 4635.7$+$ 496.02$=$ 7331.9

The total interest due in the payment is R731.44 $($ 235.42$+$ 496.02$)$