You take out an $8,200 car loan that calls for 60 monthly payments starting afte

Question

You take out an $8,200 car loan that calls for 60 monthly payments starting after 1 month at an APR of 12%. 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

a)

Rate = 0.12 / 12 = 0.01 or 1%

Present value of annuity = Annuity * [ 1 - 1 / ( 1 + r)n] / r

8,200 = Annuity * [ 1 - 1 / ( 1 + 0.01)60] / 0.01

8,200 = Annuity * 44.955038

Monthly payment = $182.40

2)

Effective interest rate = ( 1 + r/n)n - 1

Effective interest rate = ( 1 + 0.12/12)12 - 1

Effective interest rate = 1.126825 - 1

Effective interest rate = 12.68%

c)

Present value = Annuity * [ 1 - 1 / ( 1 + r)n] / r

8200 = Annuity * [ 1 - 1 / ( 1 + 0.12)4] / 0.12

8200 = Annuity * 3.037349

Annual payment = $2,699.72

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