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

Answer 1

Step 1 — trade‑in credit
2001 Odyssey value = $8,693.00
Dealer gave 85%: 0.85(8693.00) = $7,389.05

Step 2 — taxable price and sales tax
Vehicle price − trade‑in = 23,878.00 − 7,389.05 = $16,488.95
Sales tax (9.05%) = 0.0905(16,488.95) = $1,492.25

Step 3 — fees
Registration = $1,474.00
Documentation = $225.00

Step 4 — amount financed
Amount financed = 16,488.95 + 1,492.25 + 1,474.00 + 225.00 = $19,680.20

Step 5 — monthly payment
Annual rate 11.82% → monthly rate r = 0.1182/12 = 0.00985
Number of months n = 36

Monthly payment = P * r / (1 − (1 + r)^(−n))
= 19,680.20 * 0.00985 / (1 − (1.00985)^(−36))
≈ $651.97 (rounded to cents)

Step 6 — total interest paid
Total paid = 651.97 × 36 = $23,470.92
Interest = total paid − principal financed = 23,470.92 − 19,680.20 = $3,790.72

Answer: (a) $3,790.72