Question

Bill took out a 7 year loan to buy a car. If the loan carried an annual interest rate of 4.5% and he made monthly payments of $466, how much interest did he pay?

Answer 1

First, we need to compute the amount of loan taken by Bill. The monthly payments being made are an ordinary annuity. The loan amount is the present value of this annuity. The present value (PV) of an ordinary annuity (A) can be computed as follows -

where, r is the periodic rate of interest, n being no. of time periods

Monthly rate (r) = 4.5% / 12 = 0.375% or 0.00375, No. of months (n) = 7 x 12 = 84

Therefore, Loan amount = $33,524.79

Interest paid = Total payment - Loan amount = ($466 x 84) - $33,524.79 = $5,619.21