Question

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 $400. The loan will have a 8% 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.

Answer 1

PV of annuity is mathematically represented as:

P = $400, r = 8%/12 = 0.67% (monthly)

a) Financing for 48 months

n = 48

PV = 400 * 40.9619

PV = $16,384.77

This is the loan that can be afforded.

Hence maximum value of car that you can purchase = $5,000 + $16,384.77 = $21,384.8

b) Financing for 60 months

n = 60

PV = 400 * 49.3184

PV = $19,727.37

This is the loan that can be afforded.

Hence maximum value of car that you can purchase = $5,000 + $19,727.37 = $24,727.4