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

Answer 1

Trade‑in value for a 1999 Riviera (good condition) = $1,455.

Total due before trade:
- List price = $18,575.00
- Sales tax = 0.074 × 18,575 = $1,373.55
- Registration = $795.00
- Documentation = $110.00
Subtotal = 18,575 + 1,373.55 + 795 + 110 = $20,853.55

Amount financed = subtotal − trade‑in = 20,853.55 − 1,455.00 = $19,398.55

Monthly rate i = 0.1277/12 = 0.010641666666666667, n = 60 months.
Monthly payment = L * [i / (1 − (1 + i)^(−n))]
= 19,398.55 × [0.0106416666667 / (1 − (1.0106416666667)^(−60))] ≈ $439.12

Answer: $439.12 (choice b).