The Empire Carpet Company orders merchandise for $17,700, including $550 in shipping charges, from Mohawk Carpet Mills on May 4. Carpets valued at $1,390 will be returned because they are damaged. The terms of sale are 2/10, n30 ROG. The shipment arrives on May 26 and Empire wants to take advantage of the cash discount. By what date must Empire pay the invoice?

To determine the date by which Empire Carpet Company must pay the invoice to take advantage of the cash discount, we need to understand the terms of sale provided: 2/10, n30 ROG.

Let's break down the terms:
- 2/10: This means that there is a 2% discount if the invoice is paid within 10 days of the invoice date.
- n30: This means that the payment is due within 30 days of the invoice date.
- ROG: This stands for "receipt of goods" and indicates that the invoice date is the same as the date the shipment arrives.

Given these terms, here's how we can calculate the payment due date:

1. Determine the invoice date:
Since the terms state "ROG" (Receipt of Goods), the invoice date will be May 26, the same as the shipment arrival date.

2. Calculate the cash discount period:
The cash discount period is the number of days in which Empire Carpet Company can pay the invoice to receive the discount. In this case, it is 10 days.

3. Calculate the payment due date:
To calculate the payment due date, add the cash discount period to the invoice date. In this case, add 10 days to May 26.

Invoice date: May 26
Invoice date + Cash discount period: May 26 + 10 days = June 5

Therefore, Empire Carpet Company must pay the invoice by June 5 to take advantage of the cash discount.