Question

Suzanne 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 (brief):
- Monthly rate i = 0.1162/12. For 60 months, the loan principal PV given payment 455.96 is
PV = 455.96 * (1 - (1+i)^-60)/i ≈ $20,676 (approximately).
- Dealer’s total before trade-in = list price + sales tax + reg. fee + doc. fee
= 23,860*(1 + 0.0811) + 1,695 + 228 = $27,718.05.
- Trade‑in credit = total before trade-in − amount financed ≈ 27,718.05 − 20,676 ≈ $7,042.25.
- That credit is 85% of the listed trade‑in price, so listed price ≈ 7,042.25/0.85 ≈ $8,285,
which matches the 2004 Intrepid.