Question

In order to buy a car, you borrow $16,000 from a friend at 7%/year compounded monthly for 4 years. You plan to repay the loan with 48 equal monthly payments. The monthly payments are $383.14.

a) How much interest is in the 23rd payment?

b) what is the remaining balance after the 37th payment?

c) Three and a half years into the loan, you decide to pay it off. You have not made the payment due at that time. What is the payoff amount of the loan?

Answer 1

a) Here monthly payment = $383.14, Therefore, total payment amount in 23 months = 23*383.14=$8812.22

Also loan money = $16000 which is to be paid in 48 months

Therefore, loan money to be paid in 23 months = 16000/48 *23= $7666.66

Therefore, loan interest paid in 23rd payment = 8812.22-7666.66= $1145.56

b) Remaining balance after 37th payment = $383.14*(48-37) = $4214.54

c) 3.5 years = 42 months

therefore, payoff amount of the loan in 42 months = 16000*(1+0.058)⁴² = $170811.86