Question

You want to buy a car, and a local bank will lend you $40,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 10% with interest paid monthly.

1. What will be the monthly loan payment? Do not round intermediate steps. Round your answer to the nearest cent.

   $  

2. What will be the loan's EAR? Do not round intermediate steps. Round your answer to two decimal places.

   %

Answer 1

1)

Rate = 10% / 12 = 0.83333%

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

40,000 = Monthly payment * [1 - 1 / (1 + 0.0083333)⁶⁰] / 0.0083333

40,000 = Monthly payment * 47.065413

Monthly payment = $849.88

2)

EAR = (1 + APR/n)ⁿ - 1

EAR = (1 + 0.1/12)¹² - 1

EAR = (1.008333)¹² - 1

EAR = 1.1047 - 1

EAR = 0.1047 or 10.47%