Terry has just purchased a new car, which had a list price of $16,825. She had to pay 7.19% sales tax, a $1,128 vehicle registra
tion fee, and a $190 documentation fee. Terry traded in her previous vehicle, a 2003 Honda Element in good condition, and financed the rest of the cost over five years at an interest rate of 10.59%, compounded monthly. If the dealer gave Terry 90% of the listed trade-in value on her car, how much will Terry have paid in interest, once the loan is paid off? (Round all dollar values to the nearest cent, and consider the trade-in to be a reduction in the amount paid.)
Total cost of purchasing the car = $16,825 + 0.0719 x $16,825 + $1,128 + $190 = $19,352.72 Value of her previous car = 0.9 x $16,825 = $15,142.50
Amount being owed by Terry = $19,352.72 - $15,142.50 = $4,210.22
The present value of annuity is given by PV = P(1 - (1 + r/t)^-nt) / (r/t) where P is the monthly payment, r is the rate = 10.59% = 0.1059, t is the number of periods in a year = 12, n is the number of years.
