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?

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