Question

Valerie is going to purchase a new car. The car she wants has a list price of $32,495. Valerie is planning to make a down payment of $1,877. Furthermore, she plans to trade in her current car, which is a 2006 Hyundai Sonata in good condition. She will finance the rest of the cost by making monthly payments over five years. She can finance the cost at a rate of 8.64%, compounded monthly. She will also have to pay 8.23% sales tax, a $2,243 vehicle registration fee, and a $314 documentation fee. If the dealer gives Valerie 87.5% of the trade-in price on her car, listed below, approximately how much will Valerie pay in total for her new car? (Round all dollar values to the nearest cent, and consider the trade-in to be a reduction in the amount paid.)

Hyundai Cars in Good Condition
Model/Year
2004
2005
2006
2007
Sonata
$6,145
$6,520
$6,784
$7,066
Tiburon
$6,880
$7,144
$7,382
$7,785
Elantra
$4,211
$4,425
$4,598
$4,880
Accent
$5,676
$5,828
$6,005
$6,317
a.
$37,385
b.
$38,821
c.
$38,287
d.
$36,944

Answer 1

Trade-in value = 0.875·$6,784 = $5,936.00.

Assume sales tax is calculated on the full list price:
sales tax = 0.0823·$32,495 = $2,674.34.

Amount to be financed after down payment:
Principal = 32,495 + 2,674.34 + 2,243 + 314 − 5,936 − 1,877
= $29,913.34.

Monthly rate = 0.0864/12 = 0.0072, n = 60.
Monthly payment = P·r / (1 − (1+r)^(−n))
≈ 29,913.34·0.0072 / (1 − 1.0072^(−60)) ≈ $615.69.

Total of 60 payments ≈ 60·615.69 = $36,941.34.
Total Valerie pays = down payment + total financed payments ≈ 1,877 + 36,941.34 = $38,818.34 ≈ $38,821.

Answer: b.