Question

10.

PV AND LOAN ELIGIBILITY

You have saved $5,000 for a down payment on a new car. The largest monthly payment you can afford is $500. The loan will have a 9% APR based on end-of-month payments.

1. What is the most expensive car you can afford if you finance it for 48 months? Do not round intermediate calculations. Round your answer to the nearest cent.
   $  

2. What is the most expensive car you can afford if you finance it for 60 months? Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

Down payment=$5000

Monthly payment=$500

Monthly interest rate=9%/12=0.75%

PV with n=48 will be= A*(1-(1+r)^-n)/r

=500*(1-(1+0.75%)^-48)/0.75%

=500*(1-1.0075^-48)/0.0075

=500*(1-0.6986)/0.0075

=500*0.3014/0.0075

=$20092.39

Hence maximum cost will be 20092.39+5000=$25092.39

PV with n=60 will be= A*(1-(1+r)^-n)/r

=500*(1-(1+0.75%)^-60)/0.75%

=500*(1-1.0075^-60)/0.0075

=500*(1-0.6387)/0.0075

=500*0.3613/0.0075

=$24086.69

Hence maximum cost will be 24086.69+5000=$29086.69