Tom Sander is a loan officer with Miami National Bank. The bank typically charges 8% APR on loans with a compensating balance requirement of 10%. In order to be competitive with other banks, Sanders will adjust the loan rate based on a customer's compensating balance level. A customer maintaining a balance greater than 10% will get a lower interest rate and customer with a balance lower than 10% will get a higher rate.
a) What is the effective interest rate on the typical loan with a nominal 8% interest rate and a 10% compensating balance?
b) Collins construction would supply compensating balances of 150,000 and would like to borrow 2,000,000. What nominal interest rate should Sanders charge on the Collins loan in order to realize the same effective interest rate as the "typical" loan in part a?
c) Dussold Distributors would provide compensating balances of $200,000 and would like to borrow $1,000,000. What nominal interest rate should Sanders charge on the Dussold loan in order to realize the same effective interest rate as the "typical" loan in part a?
Effective rate with compensating balances (c) = Interest/(1-c)
where c is compensating balance %
A = 8/(1-0.1) ...
How to calculate effective interest rate when compensating loan is provided to obtain better nominal interest rate?