Lock Boxes. The financial manager of JAC Cosmetics is considering opening a lock box in Pittsburgh. Checks cleared through the lock box will amount to $300,000 per month. The lock box will make cash available to the company 3 days earlier.

a. Suppose that the bank offers to run the lock box for a $20,000 compensating balance. Is the lock box worthwhile?

b. Suppose that the bank offers to run the lock box for a fee of $.10 per check cleared instead of a compensating balance. What must the average check size be for the fee alternative to be less costly? Assume an interest rate of 6 percent per year.

c. Why did you need to know the interest rate to answer

(b) but not to answer (a)?