Your bank offers you a $100,000 line of credit with an interest rate of 2.5% per quarter. The loan agreement also requires that 4% of the unused portion of the credit line be deposited in a non-interest bearing account as a compensating balance. Your short-term investments are paying 1.25% per quarter. What is your effective annual interest rate if you borrow the whole $100,000 for the entire year? Assume that both the funds you borrow and the funds you invest use compound interest.

Question

Quizplus · Accepted Answer

First, let's calculate the interest expense on the $100,000 line of credit for one quarter:

Interest expense = $100,000 x 2.5% = $2,500

Next, we need to calculate the compensating balance requirement:

Compensating balance = 4% x $100,000 = $4,000

This means that we must keep $4,000 of the credit line unused and deposited in a non-interest bearing account, which is a cost to us since we could be earning interest on that money.

The effective interest rate on the loan for one quarter is:

Effective interest rate = (interest expense + compensating balance requirement) / (funds borrowed - compensating balance requirement)

Effective interest rate = ($2,500 + $4,000) / ($100,000 - $4,000)

Effective interest rate = 6.5%

Note that we subtract the compensating balance requirement from the funds borrowed to calculate the effective interest rate, since we are not paying interest on the compensating balance but we are not able to use it for investments either.

Now we need to calculate the effective annual interest rate by compounding the interest rate for four quarters:

Effective annual interest rate = (1 + quarterly rate)^4 - 1

Effective annual interest rate = (1 + 0.065)^4 - 1

Effective annual interest rate = 10.38%

Therefore, the best choice is C with an effective annual interest rate of 10.38%.

Your Bank Offers You a $100,000 Line of Credit with an Interest