Question

Which of the following one-year, $1000 bank loans offers the lowest effective annual rate?

a. A loan with an APR of 6%, compounded monthly

b. A loan with an APR of 6%, compounded annually, with a compensating balance requirement of 10% (on which no interest is paid)

c. A loan with an APR of 6%, compounded annually, with a 1% loan origination fee

Answer 1

a). EAR = [1 + (APR/m)]^m - 1; m = no. of compounding periods of the year.

= [1 + (0.06/12)]¹² - 1 = 1.0617 - 1 = 0.0617, or 6.17%

b). Effective Borrowing Amount = Loan Amount x (1 - Compensating Balance Requirement)

= $1,000 x (1 - 0.10) = $900

Interest Expense = Loan amount x interest rate = $1,000 x 0.06 = $60

EAR = Interest Expense / Effective Borrowing Amount = $60 / $900 = 6.67%

c). Interest expense = 0.06 x $1,000 = $60

Loan origination fee = 0.01 x $ 1,000 =$10.

The loan origination fee reduces the usable proceeds of the loan to $990 because it is paid at the beginning of the loan.

The interest rate per period is $70/$990 = 7.1%.

Option A offers the lowest effective annual rate.