Suppose your firm is seeking a 7-year, amortizing $100,000 loan with annual payments and your bank is offering you the choice between a $110,000 loan with a $10,000 compensating balance and a $100,000 loan without a compensating balance. If the interest rate on the $100,000 loan is 7 percent, how low would the interest rate on the loan with the compensating balance have to be in order for you to choose it?
A) 7%
B) 10%
C) 4.34%
D) not enough information is given to know

Question

Quizplus · Accepted Answer

To compare the two loan options, we need to adjust the terms of the $110,000 loan to be equivalent to a $100,000 loan. The compensating balance of $10,000 means that the bank is actually only loaning you $100,000 ($110,000 - $10,000).

The formula to calculate the equivalent interest rate between the two loans is: 
(Interest Rate with Compensating Balance) * (1 - Compensating Balance Percentage) = Interest Rate without Compensating Balance

Plugging in the numbers: 
Let x be the interest rate with compensating balance. 
(x) * (1 - 0.09) = 0.07 
x = 0.0434 or 4.34%

Therefore, the interest rate on the loan with the compensating balance would have to be 4.34% or lower for it to be a better choice than the $100,000 loan without a compensating balance.

Suppose Your Firm Is Seeking a 7-Year, Amortizing $100,000 Loan