Question

Reg has just purchased a new car. The car had a list price of $22,499, and he was responsible for 7.96% sales tax, a $2,138 vehicle registration fee, and a $262 documentation fee. Reg’s financing has an interest rate of 10.27%, compounded monthly, and a duration of three years. If Reg makes a monthly payment of $773.89, which of the following was his down payment? Round all dollar values to the nearest cent. (Note: The sales tax is applied to the full list price of the car as there is no trade-in or discount)
a.
$2,000
b.
$2,200
c.
$2,500
d.
$2,800



Please select the best answer from the choices provided


A
B
C
D

Answer 1

Compute the total purchase price, the loan amount from the monthly payment, then subtract to get the down payment.

1) Sales tax = 22499 × 7.96% = 1,790.92
Total due before down payment = 22,499 + 1,790.92 + 2,138 + 262 = 26,689.92

2) Monthly rate r = 0.1027/12 = 0.0085583333, n = 36.
Loan (present value) = PMT × (1 − (1+r)^−n)/r
Factor = (1 − (1+0.0085583333)^−36)/0.0085583333 ≈ 30.88396
Loan = 773.89 × 30.88396 ≈ 23,899.79

3) Down payment = 26,689.92 − 23,899.79 = 2,780.13 ≈ $2,780.13

Closest choice: $2,800 → D.