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%


Please select the best answer from the choices provided

A
B
C
D

Answer 1

Trade-in credit = 0.80(6591) = 5272.80
Net price = 21450 − 5272.80 = 16177.20
Sales tax = 0.0688(16177.20) = 1112.99136
Add registration and doc: principal financed P = 16177.20 + 1112.99136 + 1089 + 124 = 18503.19136

Monthly rate r = 0.1228/12 = 0.0102333333, n = 36
Monthly payment A = P·[r/(1 − (1 + r)^(−n))] ≈ $617.27
Total paid by payments = 617.27·36 ≈ $22,221.59
Total interest = 22,221.59 − 18,503.19 ≈ $3,718.40

Percent of total amount paid that is interest = 3718.40 / 22221.59 ≈ 0.1673 ≈ 16.73%

Closest choice: C (16.70%).