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 registration 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.

4,210.22 = P(1 - (1 + 0.1059/12)^-(5 x 12)) / (0.1059/12)
0.1059(4,210.22) = 12P(1 - (1.008825)^-60)
P = 445.862298 / 4.916774288 = 90.68

Amount of interest paid = 60(90.68) - 4,210.22 = 5440.80 - 4210.22 = $1230.58

╔═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╗✧   ok, now this, is epic.╚═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╝