Question 20.1: Assume that Timmons Towel and Diaper Service’s bank pays 1% ...
Assume that Timmons Towel and Diaper Service’s bank pays 1% (APR with quarterly compounding) on its compensating balance accounts. What is the EAR of Timmons’ three-month loan?
PLAN
The interest earned on the $50,000 will reduce the net payment Timmons must make to pay off the loan.
Once we compute the final payment, we can determine the implied three-month interest rate and then convert it into an EAR.
EXECUTE
The balance held in the compensating balance account will grow to 50,000(1 + 0.01/4) = $50,125.
Thus, the final loan payment will be 500,000 + 15,000 – 50,125 = $464,875. Notice that the interest on the compensating balance accounts offsets some of the interest that Timmons pays on the loan. The new cash flows are shown here on a timeline:
The actual three-month interest rate paid is:
\frac{464,875 – 450,000}{450,000}= 3.31\%Expressing this as an EAR gives 1.0331^{4} -1=13.89\%
EVALUATE
As expected, because the bank allowed Timmons to deposit the compensating balance in an interest-bearing account, the interest earned on the compensating balance reduced the overall interest cost of Timmons for the loan.