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 must pay the invoice in order to take advantage of the cash discount, we need to understand the terms of sale and calculate the appropriate time frame.

The terms of sale are given as "2/10, n30 ROG." This means that Empire can receive a cash discount of 2% if they pay within 10 days after the receipt of goods (ROG), and the full amount is due within 30 days after the receipt of goods.

To calculate the payment due date, we need to consider the date of receipt of goods. In this case, the shipment arrives on May 26. The payment due date should be within 10 days from this date to qualify for the cash discount.

Therefore, to find the payment due date, we add 10 days to the receipt of goods date:

May 26 + 10 days = June 5

So, Empire must pay the invoice by June 5 in order to take advantage of the cash discount.