Suppose your firm is seeking a seven-year, amortizing $400,000 loan with annual payments and your bank is offering you the choice between a $410,000 loan with a $10,000 compensating balance and a $400,000 loan without a compensating balance. If the interest rate on the $400,000 loan is 9.5 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)The rate would have to be lower than 8.76 percent.
B)The rate would have to be lower than 8.29 percent.
C)The rate would have to be lower than 8.14 percent.
D)The rate would have to be lower than 7.99 percent.Step 1: Find the loan payment for the loan with no compensating balance: PV = −400,000; N = 7; I = 9.5; FV = 0; = PMT = 80,814.41;

Question

Suppose your firm is seeking a seven-year, amortizing $400,000 loan with annual payments and your bank is offering you the choice between a $410,000 loan with a $10,000 compensating balance and a $400,000 loan without a compensating balance. If the interest rate on the $400,000 loan is 9.5 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)The rate would have to be lower than 8.76 percent.
B)The rate would have to be lower than 8.29 percent.
C)The rate would have to be lower than 8.14 percent.
D)The rate would have to be lower than 7.99 percent.Step 1: Find the loan payment for the loan with no compensating balance: PV = −400,000; N = 7; I = 9.5; FV = 0; => PMT = 80,814.41;

Quizplus · Accepted Answer

To find out if the loan with a compensating balance is a better option, we need to find the interest rate on that loan. We know that the loan amount is $410,000, but we also have to subtract the $10,000 compensating balance. This means that we only receive $400,000 of the loan.

Using the loan payment formula, we can calculate the loan payment for the $410,000 loan with a $10,000 compensating balance: 
PV = -$400,000 
N = 7 
PMT = ? 
I = ?

First, we need to find the future value of the compensating balance. 
FV = $10,000 x (1 + I) ^ 7

Next, we can calculate the loan payment: 
PV = -$400,000 + $10,000/(1 + I) ^ 7 
N = 7 
FV = 0 
PMT = ?

Setting the two loan payments equal to each other:

$80,814.41 = PMT x (1 - (1 + I) ^ -7)/I + $10,000/(1 + I) ^ 7 x (1 - (1 + I) ^ -7)

Using a financial calculator or trial and error, we find that the interest rate on the loan with the compensating balance would have to be lower than 8.76% for it to be a better option than the $400,000 loan without a compensating balance. Therefore, the answer is (A).

Suppose Your Firm Is Seeking a Seven-Year, Amortizing $400,000 Loan