Forty monthly payments of 200 each are needed to repay a loa

Forty monthly payments of $200 each are needed to repay a loan at an interest rate of 12% per year compounded monthly. The percentage of the amount borrowed that has been repaid by the time the thirtieth payment is made is closest to

Solution

ANSWER:

Monthly payment = $200

i =12% per annum or 12% / 12 = 1% per month

n = 40

We have to find the present value.

pv = monthly payment(p/a,i,n)

pv = 200(p/a,1%,40)

pv = 200 * 32.835

pv = 6,567

amount repaid after 13th payment = monthly payment * 13 = $200 * 13 = $2,600

% of amount borrowed that has been repaid by 13th payment = amount repaid after 13th payment / pv

% of amount borrowed that has been repaid by 13th payment = 2,600 / 6,567 = 0.3959 or 39.59%

so 39.59% has been repaid by the time 13th payment was made.