Micheal borrows 200 0 from his parents to pay for a car repa

Micheal borrows 2,00 0 from his parents to pay for a car repair. The loan is for 1 year at 2.4 interest compounded monthly. After paying 5 payments of 168.84, he decides to payoff the remaining balance all at once. How much must micheal pay?

Solution

rate per month =2.4/12%=.2%=.002=r

number of months he paid = 5=n

monthly payment=p

for the money he owes after n months={totalamount-(p/r)(1-1/(1+r)^n)}(1+r)^n={2000-(168.84/.002)(1-1/(1+.002)^5)}(1+.002)^5=(2000-839.16)(1+.002)^5=1172.50

I have basically used the concepts of present value and future value.