Question

You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $450. The loan will have a 12% APR based on end-of-month payments.
What is the most expensive car you could afford if you finance it for 48 months?What is the most expensive car you could afford if you finance it for 60 months?

Answer 1

Answer:

 48 MONTHS

PV = Down payment + $450(1 - (1 + r/m)-mn - 1)

                                                         r/m

PV = $5,000 + $450(1 - (1 + 0.12/12)-12x4 - 1)

                                            0.12/12

PV = $5,000 + $450(1 -(1 + 0.01)-48 - 1)

                                           0.01

PV = $5,000 + $450(37.9740)

PV = $5,000 + $17,088

PV = $22,088

60 MONTHS

PV = $5,000 + $450(1 - (1 + 0.12/12)-12x5 - 1)

                                            0.12/12

PV = $5,000 + $450(1 -(1 + 0.01)-60 - 1)

                                           0.01

PV = $5,000 + $450(44.9550)

PV = $5,000 + $20,230

PV = $22,230

         

Explanation:

In this case, we need to calculate the present value of the car which is a function of down payment plus the present value of the monthly payments at 12% discount rate.