Question

Bernie has decided to purchase a new car with a list price of $18,575. Sales tax in Bernie’s state is 7.40%, and he will be responsible for a $795 vehicle registration fee and a $110 documentation fee. Bernie plans to trade in his existing car, a 1999 Buick Riviera in good condition, and finance the rest of the cost for five years at an interest rate of 12.77%, compounded monthly. Assuming that the dealer gives Bernie the listed trade-in price for his car, what will his monthly payment be? Round all dollar values to the nearest cent.

Buick Cars in Good Condition
Model/Year
1998
1999
2000
2001
2002
Century
$929
$1,086
$1,150
$1,488
$1,595
LeSabre
$2,075
$2,282
$2,690
$2,935
$3,374
Regal
$1,676
$1,794
$2,030
$2,214
$2,566
Riviera
$1,291
$1,455
$1,520
$1,814
$1,959
a.
$472.05
b.
$439.12
c.
$438.20
d.
$518.23


Please select the best answer from the choices provided

A
B
C
D

Answer 1

Answer: B

Work (brief):
- Trade-in for 1999 Riviera = $1,455.
- Sales tax on full price: 0.074 × $18,575 = $1,374.55.
- Fees: $795 + $110 = $905.
- Amount to finance = 18,575 + 1,374.55 + 905 − 1,455 = $19,399.55.
- Monthly rate r = 0.1277/12 = 0.0106416667, n = 60.
- Monthly payment = (r × PV) / (1 − (1 + r)^(−n))
= (0.0106416667 × 19,399.55) / (1 − (1.0106416667)^(−60)) ≈ $439.12.