The PMI,Inc.processes an estimated 200,000 checks per year from its customers.Total revenue collected by check is $40,000,000.The average float time until the funds are credited to PMI's checking account is 6 days.For an extra cost of $ .06/check,PMI's bank will install a lock-box system that will reduce float time from 6 days to 2.5 days.If PMI earns 3.5% on its checking account,how much per check will PMI make if it uses the lock-box system?

Question

Quizplus · Accepted Answer

The savings per check from using the lock-box system can be calculated by first determining the daily interest rate, then calculating the interest saved due to the reduced float time, and finally dividing that total interest saved by the number of checks. The daily interest rate is 3.5% per year, or 3.5%/365 days = 0.00958904% per day. The interest saved per day by reducing the float time from 6 days to 2.5 days is 3.5 days. The total interest saved per check is then calculated as follows: Total revenue ($40,000,000) divided by the number of checks (200,000) gives the average amount per check ($200). The daily interest saved on this amount is $200 * 0.00958904% = $0.01917808. Over 3.5 days, this amounts to $0.01917808 * 3.5 = $0.06712328. After subtracting the cost of the lock-box system ($0.06), the net gain per check is $0.06712328 - $0.06 = $0.00712328, which rounds to $0.007 per check.