Question

Olivia is willing to pay $185 a month for four years for a car payment. if the interest rate is 4.9 percent, compounded monthly, and she has a cash down payment of $2,500, what price car can she afford to purchase?

Answer 1

Let x = the price of the car that Olivia can afford.

Down payment = $2,500
Remaining amount to be financed is P = x - 2500.

Total payments should equal the monthly payments.
The total payment over 4 years (48 months) is
A  = $185*48 = $8,880

The rate is r = 4.9% = 0.049.
The compounding interval is n = 12.
The time is t = 4  years.
The amount financed is P = $(x - 2500).
Therefore
(x - 2500)(1 + 0.049/12)⁴⁸ = 8880
1.216(x - 2500) = 8880
x - 2500 = 7302.63
x = 9802.63
Olivia can afford a car priced at $9,802.63.

Answer: $9,802.63