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.
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.
$
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. $
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
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