7.0% is the stated interest rate on the loan. Because the borrower has a compensating balance requirement, not all of the loan proceeds will be available to the borrower to use. The effective annual interest rate on a loan with a compensating balance when no interest is received on the compensating balance is the annual interest due divided by the net funds the borrower will have available to use, and it is different from the stated interest rate.
This is 20% minus 7%. That is not the correct way to find the answer to this question. The correct way to calculate the effective annual rate on this loan is to first calculate the annual interest that will be due on $100,000 at a stated rate of 7% for one year. Then, find the net funds from the loan the borrower will have available after deducting the compensating balance requirement. The effective annual interest rate on a loan with a compensating balance when no interest is received on the compensating balance is the annual interest due divided by the net funds the borrower will have available to use.
The annual interest on $100,000 at a stated interest rate of 7% is $7,000 ($100,000 × .07). The net available funds to the borrower if a 20% compensating balance is required is 80% of $100,000, or $80,000. The effective annual interest rate on a loan with a compensating balance when no interest is received on the compensating balance is the annual interest due divided by the net funds the borrower will have available to use. Thus the effective annual interest rate on the loan is $7,000 ÷ $80,000, which equals .0875 or 8.75%.
This is 7% × 1.20. This is not the correct way to find the answer to this question. The correct way to calculate the effective annual rate on this loan is to first calculate the annual interest that will be due on $100,000 at a stated rate of 7% for one year. Then, find the net funds from the loan the borrower will have available after deducting the compensating balance requirement. The effective annual interest rate on a loan with a compensating balance when no interest is received on the compensating balance is the annual interest due divided by the net funds the borrower will have available to use.
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