Question

Would it be worth it to incur a compensating balance of $10,000 in order to get a 1 percent lower interest rate on a one-year, discount interest loan of $225,000? Show your calculations to justify your answer.

Answer 1

No, it will not be worth to incur a compensating balance of $10,000 in order to get a 1 percent lower interest rate on a one-year, discount interest loan of $225,000.

Calculations and explanations:

It depends upon whether $225,000 × (1 + i) or $235,000 × (1 + [i – 0.01]) is larger. The compensating balance for the lower loan rate will make sense if:

225,000*(1+i)>235,000*(1+(i-0.01))

or 225,000/235,000*(1+i)>(1+(i-0.01))

or 0.9574+0.9574i>1+i-0.01

or -0.0426i>0.0326

or i<-76.5%

In other words, only if the rate is less than -76.50 percent will it make sense to accept the lower rate. Since this is not likely to happen, the lower rate associated with the compensating balance isn’t worth it.