Question

You have saved $4000 for a down payment on a new car. The largest monthly payment you can afford is $350. The loan will have a 12% APR based on end-of-months payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months?

Note: Show your full calculation, dont used Excel or any other calculator

Answer 1

Part 1: Loan that can be afforded using 48 month financing

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

where rate = 12%/12 = 1% per month

= 350*(1-1/(1+1%)^48)/ 1%

=13290.89

Value ofcar = Loan + down payment

= 13290.89+ 4000

= 17290.89

Part 2

Loan that can be afforded using 60 month financing

PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

where rate = 12%/12 = 1% per month

= 350*(1-1/(1+1%)^60)/ 1%

=15734.26

Value of car = Loan + down payment

= 15734.26 + 4000

= $ 19734.26