What interest rate would make it worthwhile to incur a compensating balance of $

Question

What interest rate would make it worthwhile to incur a compensating balance of $15,000 in order to get a 0.65 percent lower interest rate on a 2 year, pure discount loan of $225,000? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)

What interest rate would make it worthwhile to incur a compensating balance of $15,000 in order to get a 0.65 percent lower interest rate on a 2 year, pure discount loan of $225,000? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)

Explanation / Answer

Amount of Discount Loan = $ 225,000
Period = 2 years

interst rate = i

The Effective Annual rate r can be calculated using the formula

r = Principal * interest rate * no of years / Principal * (1 -i)
= (225000 * 2 * i) / 225000 * (1-i)

r = 2 * i / (1-i)

The effective annual rate where a compensating balnce of $ 15000 is to be maintained can be calculated using the formula

r1 = (Principal * interest rate * no of years) / Principal * (1-(compensating balance/Principal))

= 225000 * i * 2 / 225000 (1-(15000/225000)) = 2*i / (1-0.06667)

Now r1 is given as r(1-0.0065) as by maintaining the compensating balance the interest rate can be lowered by 0.65% (or 0.0065) that means

2*i / (1-i) = (2*i/0.9333) (1-0.0065)

2i / (1-i) = 2*i * 0.9935/ 0.9333 -> 1/(1-i) = 1.06450

1-i = 1/1.06450 -> i = 1- (1/1.06450) = 1 - 0.93941 = 0.060592

There fore the interest rate i = 6.0591 or 6.06%

This is the intereset rate at which the discount loan can be provided without compensating balance.

If an amount $ 15000 is provided as a compensating balance, then the interest rate at which the loan should become worthwile will be 6.06 - 0.65 = 5.41%

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