You take out an $8,600 car loan that calls for 48 monthly payments starting afte

Question

You take out an $8,600 car loan that calls for 48 monthly payments starting after 1 month at an APR of 6%. a. What is your monthly payment? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Monthly payment b. What is the effective annual interest rate on the loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Effective annual interest rate c. Now assume the payments are made in four annual year-end installments. What annual payment would have the same present value as the monthly payment you calculated? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Annual payment

Explanation / Answer

Answer a.

Amount borrowed = $8,600
Annual Interest Rate = 6%
Monthly Interest Rate = 0.50%
Period = 48 months

Monthly Payment * PVIFA(0.50%, 48) = $8,600
Monthly Payment * (1 - (1/1.005)^48) / 0.005 = $8,600
Monthly Payment * 42.58032 = $8,600
Monthly Payment = $201.97

Answer b.

Effective Annual Interest Rate = (1 + Monthly Interest Rate)^12 - 1
Effective Annual Interest Rate = (1 + 0.005)^12 - 1
Effective Annual Interest Rate = 1.0617 - 1
Effective Annual Interest Rate = 0.0617 or 6.17%

Answer c.

Amount borrowed = $8,600
Annual Interest Rate = 6.17%
Period = 4 years

Annual Payment * PVIFA(6.17%, 4) = $8,600
Annual Payment * (1 - (1/1.0617)^4) / 0.0617 = $8,600
Annual Payment * 3.45166 = $8,600
Annual Payment = $2,491.56

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