Question

A man bought a car which costs GH¢500,000 from a dealer on hire purchase. He pays a deposit of GH¢300,000 and agree to pay the balance at 8% compound interest per annum. He also agrees to pay GH¢100,000 at the end of each year, for the next two years.

(a) Calculate the total amount left to be paid per the agreement.

(b) How much will be remaining to be paid after two years?

Answer 1

Here, the car initially costs = 500,000 units.

Since, he already paid 300,000 units so the remaining (500,000 - 300,000) units = 200,000 units is to be paid.

So, the original principal sum = P = 200,000 units.

The agreements he made are - 1. Pay the balance of 200,000 units at 8% compound interest compounded annually. 2. Pay 100,000 units at the end of each year, for the next two years.

a ) The formula for compound interest is given by , P' = P ( 1 + (r/n) )nt , where, P = original principal sum P' = new principal sum r = nominal annual interest rate n = compounding frequency t = overall length of time the interest is applied

Plugging in the values of P = 200,000, r = 8% = 0.08, n = 1(since annually), t = 2 we obtain the value of P' as, P' = 200000 * ( 1+(0.08/1))1*2 = 233,280 units

So the total amount to be paid per the agreement = 233,280 units

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b ) He agrees to pay 100,000 units at the end of each year. So by the end of two years the amount remaining to be paid = total amount to be paid - total amount already paid in two years. = { 233,280 - (100,000 + 100,000) } units = 33,280 units.

33,280 units will be remaining to be paid after two years.