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


Please select the best answer from the choices provided

A
B
C
D

Answer 1

B

Work (rounded to cents):
- Trade-in credit = 0.875(6784.00) = $5,936.00
- Sales tax (on list price) = 0.0823(32,495.00) = $2,674.34
- Amount to be financed = 32,495.00 + 2,674.34 + 2,243.00 + 314.00 − 5,936.00 − 1,877.00 = $29,913.34
- Monthly rate = 0.0864/12 = 0.0072, n = 60
- Monthly payment = P * [i / (1 − (1+i)^{-n})] ≈ 29,913.34 * 0.020584 ≈ $615.74
- Total of 60 payments ≈ 60(615.74) = $36,944.16
- Total paid = down payment + total loan payments ≈ 1,877.00 + 36,944.16 = $38,821.16 ≈ $38,821

Therefore answer B.