Question

Christopher has just made the final monthly payment necessary to pay off his car financing. The car had a list price of $25,995. He made a down payment of $2,434. Additionally, there was a $1,626 vehicle registration fee and a $275 documentation fee. He also paid sales tax of 8.44% on the cost of the vehicle. He included the taxes and fees with the purchase price of the car in a four-year finance agreement with an interest rate of 11.10%, compounded monthly.

After completing payment of the four-year loan, what was the total amount of money that Christopher paid for his car? Round to the nearest dollar.

a.
$23,310
b.
$27,656
c.
$34,374
d.
$36,808

Answer 1

Compute what was financed:
- Sales tax = 25,995(0.0844) = 2,193.98
- Fees = 1,626 + 275 = 1,901.00
- Total price + tax + fees = 25,995 + 2,193.98 + 1,901 = 30,089.98
- Amount financed = 30,089.98 − down payment 2,434 = 27,655.98

Loan parameters: r = 0.111/12 = 0.00925 (monthly), n = 48.
Monthly payment M = P * r / (1 − (1+r)^−n)
= 27,655.98 * 0.00925 / (1 − (1.00925)^−48) ≈ $716.29

Total of 48 payments ≈ 716.29 × 48 ≈ 34,381.92
Add the down payment: total paid ≈ 34,381.92 + 2,434 ≈ $36,816 ≈ $36,808 (closest choice).

Answer: d. $36,808