A bank offers your firm a revolving credit arrangement for up to $85 million at an interest rate of 2.5 percent per quarter. The bank also requires you to maintain a compensating balance of 4 percent against the unused portion of the credit line, to be deposited in a non-interest-bearing account. Assume you have a short-term investment account at the bank that pays 10 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans.



Your effective annual interest rate (an opportunity cost) on the revolving credit arrangement if your firm does not use it during the year is percent

The way I was taught to do this was
1.7^3-1 which would equal 39.13. That is not the answer. Is 1.7 not the number used?

To determine the effective annual interest rate on the revolving credit arrangement, you need to consider both the interest rate and the compensating balance requirement.

The interest rate on the revolving credit arrangement is given as 2.5 percent per quarter. To convert this to an annual interest rate, you need to consider that there are four quarters in a year. So, the annual interest rate on the credit arrangement is:

2.5% x 4 = 10% per year

Now, let's consider the compensating balance requirement. The bank requires you to maintain a compensating balance of 4 percent against the unused portion of the credit line. This means that you need to set aside a portion of the credit line, equal to 4 percent of $85 million, in a non-interest-bearing account.

Compensating balance = 4% x $85 million = $3.4 million

So, you need to set aside $3.4 million in a non-interest-bearing account, which means you cannot invest this amount and earn any interest.

Now, to calculate the effective annual interest rate, we need to consider the opportunity cost of not being able to invest this $3.4 million. You mentioned that you have a short-term investment account at the bank that pays 10% per quarter.

The opportunity cost is the interest you could have earned on the $3.4 million in the short-term investment account. We can calculate this by multiplying the interest rate by the number of quarters in a year:

Opportunity cost = 10% x 4 = 40% per year

Therefore, the effective annual interest rate on the revolving credit arrangement, considering the interest rate and the compensating balance requirement, is 40%.