Problema Solution
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.
a.
$2,000
b.
$2,200
c.
$2,500
d.
$2,800
Answer provided by our tutors
P = 22499*(1 + 0.0796) + 2138 + 262
P = $26,689.92 present value
i = 0.1027/12 interest rate per period
n = 12*3 = 36 periods
R = periodic payment
R = P*i/(1 - (1 + i)^(-n))
R = 26689.92*(0.1027/12)/(1 - (1 + (0.1027/12))^(-36)
R = $864.60
Reg makes a monthly payment of $773.89 means he will have to make a down payment of:
36*(864.60 - 773.89) = $3,265.56