Suppose your firm is seeking a three year, amortizing $340,000 loan with annual

Question

Suppose your firm is seeking a three year, amortizing $340,000 loan with annual payments and your bank is offering you the choice between a $352,000 loan with a $12,000 compensating balance and a $340,000 loan without a compensating balance. The interest rate on the $340,000 loan is 9.5 percent. How low would the interest rate on the loan with the compensating balance have to be for you to choose it? (Do not round intermediate calculations and round your final answer to 2 decimal places.) Interest rate %

Explanation / Answer

Hi,

Please find the detailed answer as follows:

Step 1: Calculate Annul Payment for 340000 Loan

Nper = 3 (indicates the period)

Rate = 9.5% (indicates the rate of interest)

PV = 340000 (indicates the amount of loan)

FV = 0 (indicates future value, if any)

PMT = ? (indicates the annual payment)

Annual Payment = PMT(Rate,Nper,PV,FV) = PMT(9.5%,3,-340000,0) = $135517.19

Step 2: Calculate Interest Rate for the Amount with Compensating Balance

Nper = 3 (indicates the period)

PMT = 135517.19 (indicates the annual payment)

PV = 352000 (indicates the amount of loan)

FV = 0 (indicates future value, if any)

Rate = ? (indicates the rate of interest)

Interest Rate = Rate(Nper,PMT,PV,FV) = Rate(3,135517.19,-352000,0) = 7.57%

Answer is 7.57%.

Thanks.

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