Suppose your firm is seeking a five year, amortizing $300,000 loan with annual p
ID: 2783050 • Letter: S
Question
Suppose your firm is seeking a five year, amortizing $300,000 loan with annual payments and your bank is offering you the choice between a $310,000 loan with a $10,000 compensating balance and a $300,000 loan without a compensating balance. The interest rate on the $300,000 loan is 10.0 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.)
Suppose your firm is seeking a five year, amortizing $300,000 loan with annual payments and your bank is offering you the choice between a $310,000 loan with a $10,000 compensating balance and a $300,000 loan without a compensating balance. The interest rate on the $300,000 loan is 10.0 percent.
Explanation / Answer
Annual instalment under the loan without compensating balance = 300000*0.10*1.1^5/(1.1^5-1) = $ 79,139.24 Less: Annualized value of the return of compensating balance = 10000*0.10/(1.1^5-1) = $ 1,637.97 Net instalment that can be paid on the loan with compensating balance, for both the loans to be of equal value = $ 77,501.27 The interest rate on the loan with compensating balance can be found out from the following equation: 310000 = 77501.27*PVIFA(r,5), where r is the equivalent interest rate Solving for r 3.9999 = PVIFA(r,5) The interest factors for 7% and 8% are given below: 7% 8% 4.1002 3.9927 So r lies between 7% and 8% Using simple interpolation r = 7+(4.1002-3.999)/(4.1002-3.9927) = 7.94% At an interest rate of 7.94 for the loan with compensating balance one would be indifferent between the loans. If the loan with compensating balance is to be chosen, the interest rate should be 7.93% 7.93% Answer
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