Question

Renee is going to buy a new car that has a list price of $19,675. She will be responsible for $1,420 in vehicle registration fees, $85 in documentation fees, and 8.92% sales tax. She plans to trade in her current car, a 2002 Buick LeSabre in good condition, and finance the rest of the cost over four years at an interest rate of 11.34%, compounded monthly. If the dealer gives Renee 85% of the listed trade-in value for her car, what will her 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.
$521.96
b.
$508.80
c.
$518.80
d.
$504.46

Answer 1

Step 1 — Trade‑in allowance
2002 LeSabre listed value = $3,374
Dealer gives 85% → trade‑in allowance = 0.85(3374) = $2,867.90

Step 2 — Costs and tax
Sales tax = 8.92% of the list price = 0.0892(19,675) = $1,755.01
Registration + documentation = $1,420 + $85 = $1,505.00

Total to finance = list price + tax + fees − trade‑in
= 19,675 + 1,755.01 + 1,505.00 − 2,867.90
= $20,067.11

Step 3 — Monthly payment on a 4‑year (48‑month) loan at 11.34% APR (monthly rate = 0.1134/12 = 0.00945)

Monthly payment formula: M = P·i / (1 − (1+i)^−n)
P = 20,067.11, i = 0.00945, n = 48

M ≈ 20,067.11(0.00945) / (1 − (1.00945)^−48) ≈ $521.96

Answer: (a) $521.96