A bank offers your firm a revolving credit arrangement for up to $70 million at

Question

A bank offers your firm a revolving credit arrangement for up to $70 million at an interest rate of 1.9 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 that you have a short-term investment account at the bank that pays 1.05 percent per quarter, and assume that the bank uses compound interest on its revolving credit loans.

What is your effective annual interest rate on the lending arrangement if you borrow $70 million immediately and repay it in one year?

Explanation / Answer

The company is taking a loan of $70 million for one year. Interest is paid on quarterly compounded basis. Thus company has to pay after one year:

$70 million x (1.019)4=$70 million x 1.07819= $75.4735 million

Thus interest paid on loan is $75.4735-$70= $5.4735 million

Further he has to deposit 4% of the amount in a non interest bearing account. He has the scope of depositing this money in a short investment account which can yield quarterly intererst of 1.05 percent. Thus by depositing it in non paying account he is lossing opportunity to earn this interest. Assuming interest is received on simple interest basis, he has lost interest:

$70 million x4%x1.05%x4 quarters=0.1176 million

Thus effectively he is paying interest of 5.4735 million +0.1176 million = 5.5911 million

Therefore, Annual rate of this interest on 70 million is:

(5.5911*100) / 70 = 7.9 % approx.

Result: Answer of option C is correct

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