Question

uzanne has purchased a car with a list price of $23,860. She traded in her previous car, which was a Dodge in good condition, and financed the rest of the cost for five years at a rate of 11.62%, compounded monthly. The dealer gave her 85% of the listed trade-in price for her car. She was also responsible for 8.11% sales tax, a $1,695 vehicle registration fee, and a $228 documentation fee. If Suzanne makes a monthly payment of $455.96, which of the following was her original car?

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.
2004 Intrepid
b.
2008 Neon
c.
2005 Viper
d.
2007 Dakota

Answer 1

Answer: a. 2004 Intrepid

Work:
- Monthly rate r = 0.1162/12.
- Present-value factor for 60 months: PVFA = (1 - (1+r)^-60)/r.
- Loan principal L = monthly payment × PVFA = 455.96 × PVFA ≈ $20,677.696.

Write financed amount as:
financed = list price + sales tax(on the list price) + registration + doc fee − trade‑in credit
= 23860 + 0.0811(23860) + 1695 + 228 − 0.85·(listed trade‑in value)
= 27719.946 − 0.85·(listed trade‑in value).

Set this equal to L and solve for the listed trade‑in value:
0.85·(listed value) = 27719.946 − 20677.696 = 7042.25
listed value = 7042.25 / 0.85 = 8285.

8285 is the listed value for the 2004 Intrepid, so Suzanne’s original car was the 2004 Intrepid.