Question

Charles is going to purchase a new car that has a list price of $21,450. He is planning on trading in his good-condition 2004 Dodge Neon and financing the rest of the cost over three years, paying monthly. His finance plan has an interest rate of 12.28%, compounded monthly. Charles will also be responsible for 6.88% sales tax, a $1,089 vehicle registration fee, and a $124 documentation fee. If the dealer gives Charles 80% of the listed trade-in price on his car, once the financing is paid off, what percent of the total amount paid will the interest be? (Consider the trade-in to be a reduction in the amount paid.)

Dodge Cars in Good Condition
Model/Year
2004
2005
2006
2007
2008
Viper
$7,068
$7,225
$7,626
$7,901
$8,116
Neon
$6,591
$6,777
$6,822
$7,191
$7,440
Intrepid
$8,285
$8,579
$8,699
$9,030
$9,121
Dakota
$7,578
$7,763
$7,945
$8,313
$8,581
a.
17.64%
b.
15.67%
c.
16.70%
d.
12.86%

Answer 1

Total price before trade-in = 21450 + 0.0688(21450) + 1089 + 124
= 21450 + 1475.76 + 1089 + 124 = 24138.76.

Trade‑in credit = 0.80(6591) = 5272.80.

Amount financed (principal) = 24138.76 − 5272.80 = 18865.96.

Monthly rate r = 0.1228/12 = 307/30000 ≈ 0.0102333333, n = 36 months.
Total paid by monthly payments = P * [n r / (1 − (1+r)^(−n))].

The fraction of the total paid that is interest equals 1 − (principal / total payments)
= 1 − 1 / [n r / (1 − (1+r)^(−n))].

Evaluating this gives ≈ 0.1670 = 16.70%.

Answer: c. 16.70%