A mail-order company processes 8,200 checks per month. Of these, 64 percent are for $39 while the remainder are for $69. The $39 checks have a collection delay of 2.1 days on average while the $69 checks are delayed 1.8 days on average. Assume each month has 30 days. The interest rate is 5.2 percent per year. What is the maximum amount that should be paid to reduce the weighted average float to 1.5 days?

Question

Quizplus · Accepted Answer

First, calculate the number of $39 and $69 checks: $39 checks = 64% of 8200 = 5248 checks, $69 checks = 36% of 8200 = 2952 checks. Then, calculate the daily float for each type of check: $39 checks float = 5248 checks * $39/check * 2.1 days = $429,739.2, $69 checks float = 2952 checks * $69/check * 1.8 days = $366,110.4. The total float = $429,739.2 + $366,110.4 = $795,849.6. The daily interest rate = 5.2% / 365 = 0.014246575%. To reduce the weighted average float to 1.5 days, calculate the new total float = (5248 * $39 + 2952 * $69) * 1.5 days = $597,637.2. The difference in float = $795,849.6 - $597,637.2 = $198,212.4. The maximum amount to be paid = $198,212.4 * 0.014246575% = $6,130.

A Mail-Order Company Processes 8,200 Checks Per Month