A bank lends a firm $500,000 for one year at 8 percent and requires compensating balances of 10percent of the face value of the loan. The effective annual interest rate associated with this loan is

Question

Quizplus · Accepted Answer

The effective annual interest rate (EAR) takes into account any fees, such as the compensating balance requirement, charged by the lender when calculating the actual annual cost of borrowing.

To calculate the EAR in this scenario, we need to determine the actual amount borrowed after factoring in the compensating balance requirement.

Compensating balance = 10% x $500,000 = $50,000
Actual amount borrowed = $500,000 - $50,000 = $450,000

Using the formula for EAR:

EAR = (1 + APR/n)^n - 1
where APR is the annual percentage rate (in decimal form) and n is the number of compounding periods per year.

APR = 8%
n = 1 (since the loan is for one year)

EAR = (1 + 0.08/1)^1 - 1
EAR = 0.08 or 8%

However, since the loan requires a compensating balance of 10%, the actual annual cost of borrowing is higher than 8%.

To adjust for the compensating balance, we can use the following formula:

Adjusted APR = APR / (1 - Compensating balance rate)
Adjusted APR = 0.08 / (1 - 0.1)
Adjusted APR = 0.089 or 8.9%

Therefore, the effective annual interest rate associated with this loan is 8.9%, which is option C.

A Bank Lends a Firm $500,000 for One Year at 8