Audrey is buying a new car for $32,998.00. She plans to make a down payment of $4,200.00. If she's to make monthly payments of $525 for the next five years, what APR has she paid?

A. 37%

B ...37%

C. 3%

D. 3.7%

This question is an annuity problem with cost of the car = $32,998, the present value of the annuity (PV) is given by the difference between the cost of the car and the down payment = $32,998 - $4,200 = $28,798. The monthly payments (P) = $525 and the number of number of years (n) = 5 years and the number of payments in a year (t) is 12 payments (i. e. monthly) The formula for the present value of an annuity is given by PV = (1 - (1 + r/t) ^-nt) / (r/t) 28798 = 525 (1 - (1 + r/12) ^ - (5 x 12)) / (r/12) 28798r / 12 = 525 (1 - (1 + r/12) ^-60) 28798r / (12 x 525) = 1 - (1 + r/12) ^-60 2057r / 450 = 1 - (1 + r/12) ^-60 Substituting option A (r = 37% = 0.37) 2057r / 450 = 2057 (0.37) / 450 = 761.09 / 450 = 1.691 1 - (1 + r/12) ^60 = 1 - (1 + 0.37/12) ^-60 = 1 - 0.1617 = 0.8383 Therefore, r is not 37% Substituting option D (r = 3.7% = 0.037) 2057r / 450 = 2057 (0.037) / 450 = 76.109 / 450 = 0.1691 1 - (1 + r/12) ^60 = 1 - (1 + 0.037/12) ^-60 = 1 - 0.8313 = 0.1687 Therefore, r is approximately 3.7%