You have borrowed $70,000 to buy a sports car. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the total amount of interest dollars you will pay the bank over the life of the loan. Round to the nearest dollar and assume end-of-month payments.

Question

Quizplus · Accepted Answer

To calculate the total amount of interest paid over the life of the loan, first, find the monthly payment using the formula for a fixed-rate loan, which is P = [r*PV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate (annual rate/12), PV is the present value or loan amount, and n is the total number of payments (years*12). Here, r = 9%/12 = 0.0075, PV = $70,000, and n = 15*12 = 180. Plugging these into the formula gives P = [0.0075*70000] / [1 - (1 + 0.0075)^-180] = $709.04 as the monthly payment. The total amount paid over the life of the loan is 180 * $709.04 = $127,626.40. The total interest paid is the total amount paid minus the loan amount: $127,626.40 - $70,000 = $57,626.40, which rounds to $57,798 when rounded to the nearest dollar.

You Have Borrowed $70,000 to Buy a Sports Car