Question

Suppose your firm is seeking a four year, amortizing $260,000 loan with annual payments and your bank is offering you the choice between a $268,000 loan with a $8,000 compensating balance and a $260,000 loan without a compensating balance. The interest rate on the $260,000 loan is 9.8 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

%

Answer 1

Answer: 9.38% Workings and explanation The annual installment on the $260000 loan = 260000*0.098*1.098A4/(1.09844-1) - 81,667.58 For the firm to be indifferent between the two options, the maximum that the firm would be willing to pay for the loan with the compensatory balance is 81667.58, 81667.58, 81667.58 and 81667.58+8000 for the four years Then, $268,000 will be the PV of the above payments Equating, we have 268000 81667.58*PVIFA(r,4)+8000*PVIF(r,4) The value of r has to be found out by trial and error. Using 10% -81667.58*3.16987+8000*0.68301- Using 9% 81667.58*3.23972++8000 0.70843- The value of r lies between 9% and 10%. It can be found out by simple interpolation as shown below: r-9+(270247.53-268000)/(270247.53-264339.69)- At 9.38% the loan with compensatory balance would be equal to the loan without compensatory balance. The loan with compensatory balance would be preferred if the interest on it is less than 9.38% 264339.69 270247.53 9.38