Question

Dennis has just made the final monthly payment necessary for paying off his car financing. When he purchased the car three years ago, it had a list price of $23,878. Dennis traded in his good-condition 2001 Honda Odyssey and financed the rest of the cost at an interest rate of 11.82%, compounded monthly. The dealer gave Dennis 85% of the trade-in value of his car, listed below. Dennis was also responsible for paying 9.05% sales tax, a $1,474 vehicle registration fee, and a $225 documentation fee. Sales tax was calculated after subtracting the trade-in credit from the vehicle price. All told, how much did Dennis pay in interest? (Round all dollar values to the nearest cent, and consider the trade-in to be a reduction in the amount paid.)
Honda Cars in Good Condition
Model/Year
2000
2001
2002
2003
Element
$5,887
$6,080
$6,225
$6,622
Odyssey
$8,450
$8,693
$8,928
$9,224
Insight
$4,384
$4,661
$5,006
$5,440
Accord
$6,356
$6,626
$6,817
$7,114

a.
$3,790.72
b.
$3,906.80
c.
$4,599.44
d.
$3,668.52



Please select the best answer from the choices provided


A
B
C
D

Answer 1

A

Work (brief):
- Trade-in credit = 0.85·$8,693 = $7,389.05
- Taxable price = $23,878 − $7,389.05 = $16,488.95
- Sales tax = 9.05%·$16,488.95 = $1,492.25
- Amount financed = $16,488.95 + $1,492.25 + $1,474 + $225 = $19,680.20
- Monthly rate = 0.1182/12 = 0.00985, n = 36
- Monthly payment M = P·i/(1−(1+i)^(−n)) ≈ $651.98
- Total paid = 36·M ≈ $23,471.14, interest = $23,471.14 − $19,680.20 ≈ $3,790.72

So answer a.