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

Answer 1

Total price = list price + sales tax + registration + doc fee
= $22,499 + 0.0796(22,499) + $2,138 + $262
sales tax = 22,499(0.0796) = $1,790.92
Total price = $22,499 + $1,790.92 + $2,138 + $262 = $26,689.92

Let L = amount financed. Monthly rate r = 0.1027/12 = 0.0085583333333, n = 36.
Monthly payment formula: 773.89 = L * r / (1 - (1+r)^(-36))
=> L = 773.89 * (1 - (1+r)^(-36)) / r ≈ $23,900.85

Down payment = Total price − L = $26,689.92 − $23,900.85 = $2,789.07 ≈ $2,800

Answer: d. $2,800.