Two customers purchased $315 of merchandise from the same store on account. The terms of both sales were 3/15, n/45. Interest charged after 45 days is 1% per month. The first customer paid $305.55, and the second customer paid $315. Yet both of their accounts were marked paid in full. Why?

So the first customer paid within the first 15 days of purchase and got a discount.

The second customer perhaps settled his account  after the 15th day of purchase but not later than the 45th day.

Explanation:

The term 3/15, n/45 simply implies that customers are expected to settle their bills on or before the 45 day after purchases. However, customers will get a discount of 3% off the invoice value provided they pay at a date within the first 15 days of purchase.

Hence, whoever pays before the 15th day  will have to pay a net amount less discount. This equals

(100-3)% × $315 = $305.55

So the first customer paid within the first 15 days of purchase and got a discount.

The second customer paid the full invoice price of $315. Perhaps he settled his account  after the 15th day of purchase but not later than the 45th day, So he got no discount

The first customer paid within 15 days and that is why he paid $305.55 because enjoyed 3% discount.

But the second customer paid the full amount due within 45 days because he failed to pay within 15 days to enjoy 3% discount.

Explanation:

In the question, the terms 3/15, n/45 simple that any customer that pays within 15 days will receive 3% discount while the customer will have to pay the full amount due in 45 days if he fails to pay within 15 days. In addition, any payment after 45 days will attract 1% interest per month.

Based on the above, we can have the following from the question:

Payment due within 15 days = $315 – ($315 * 3%) = $315 - $9.45 = $305.55

Payment due within 45 days = $315 i.e. full payment

Payment due after 45 days = $315 plus 1% interest monthly  

Therefore, it can be seen from the above that the first customer paid within 15 days and that is why he paid $305.55, while the second customer paid the full amount due within 45 days because he failed to pay within 15 days to enjoy 3% discount.