Question

You want to buy a car, and a local bank will lend you $10,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 7% 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

Monthly Loan Payment

Period for Ammortization = 60 Months (Given)

Nominal Interest Rate = 7% (Given)

Monthly Interest Rate = 0.07/12 = 0.58333333%

Let Monthly Payment = M

We know, Present Value of Monthly Payments = $10,000

Thus,

M * PVAF(60, 0.5833%) = 10,000

M * 50.50199354 = 10,000

M = 10,000/50.50199354

M = $198.011985

Effective Annual Rate

Nominal Interest Rate = 7% (Given)

Compounding Periods per annum = Monthly = 12 per annum

Let, Nominal Interest Rate = i = 7%

And, Compounding Periods = n = 12

EAR = [(1 + (i/n))^n] - 1

EAR = [(1 + (0.07/12))^12] - 1

EAR = [(1.0058333333^12] - 1

EAR = 1.07229008 - 1

Effective Annual Rate = 7.229008%