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?

Question

Quizplus · Accepted Answer

To find the price of the car Olivia can afford, we need to calculate the present value of the annuity (monthly payments) and add the down payment. The formula for the present value of an annuity is:  PV = PMT × [(1 - (1 + r)^-n) / r]  Where PMT is the monthly payment ($185), r is the monthly interest rate (4.9% annual rate / 12 months = 0.0040833), and n is the total number of payments (4 years × 12 months = 48).  PV = 185 × [(1 - (1 + 0.0040833)^-48) / 0.0040833]  PV ≈ $8,049.07  Adding the down payment of $2,500 gives a total car price of $10,549.07.

Olivia Is Willing to Pay $185 a Month for Four