How much time must be saved to justify a lock-box system that processes 350 cheques per day at an average amount of $400 per cheque if the system will cost $20,000 annually and interest rates average 8 percent?

Question

Quizplus · Accepted Answer

The total amount processed daily through cheques is 350 cheques * $400 = $140,000. At an 8% interest rate, the daily interest is $140,000 * 0.08 / 365 = $30.68. The annual cost of the lock-box system is $20,000, so to justify this cost, $20,000 / $30.68 ≈ 652 days of interest savings are needed. However, since the question asks how much time must be saved, and considering the daily processing, the calculation should reflect the time saved in processing these cheques faster due to the lock-box system. The correct interpretation involves dividing the annual cost by the daily interest benefit to find the number of days' worth of interest the annual fee represents, which is then converted into the time saved by faster processing. The error in the initial explanation was in misinterpreting the final step as needing 652 days of interest savings, which doesn't align with the provided options or the correct approach to answering the question. The correct approach involves understanding that the annual cost savings must equal the annual cost of the lock-box system, and the calculation should directly relate the cost savings per day to the annual cost.

How Much Time Must Be Saved to Justify a Lock-Box