Question

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 15% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months? Do not round intermediate calculations. Round your answers to the nearest cent.

Financed for 48 months: $

Financed for 60 months: $

Answer 1

a. The amount is computed as follows:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 15% / 12

= 1.25%

So, the amount will be as follows:

= $ 500 x [ (1 - 1 / (1 + 0.0125)⁴⁸ ) / 0.0125 ]

= $ 500 x 31.32693316

= $ 15,663.46658

So, the amount will be as follows:

= $ 15,663.46658 + $ 5,000

= $ 20,663.47

b. The amount is computed as follows:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 15% / 12

= 1.25%

So, the amount will be as follows:

= $ 500 x [ (1 - 1 / (1 + 0.0125)⁶⁰ ) / 0.0125 ]

= $ 500 x 42.03459179

= $ 21,017.2959

So, the amount will be as follows:

= $ 21,017.2959 + $ 5,000

= $ 26,017.30

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