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

Answer: c. 16.70%

Work (brief):
- Trade‑in value = 80% of $6,591 = $5,272.80.
- Taxable purchase after trade‑in = $21,450 − $5,272.80 = $16,177.20.
- Sales tax = 6.88% of $16,177.20 = $1,112.99.
- Other fees = $1,089 + $124 = $1,213.
- Amount to finance (principal) = $16,177.20 + $1,112.99 + $1,213 = $18,503.19.

Loan: 36 monthly payments, monthly rate r = 0.1228/12 = 0.010233333...
Monthly payment PMT = P * [r/(1 − (1+r)^−36)] ≈ $18,503.19 * 0.033360 ≈ $617.27.
Total paid by monthly payments = 36 * $617.27 ≈ $22,221.58.
Total interest = $22,221.58 − $18,503.19 ≈ $3,718.39.

Percent of total amount paid that is interest = 3,718.39 / 22,221.58 ≈ 0.1670 ≈ 16.70% (choice c).