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 to take advantage of the cash discount, we need to understand the terms of sale mentioned in the question.

The terms of sale mentioned are 2/10, n30 ROG. This means that a 2% cash discount is offered if the payment is made within 10 days of the invoice date. If the payment is not made within the discount period, the full amount is due within 30 days of the invoice date (n30).

Given that the shipment arrives on May 26, we need to calculate the date by which Empire must pay the invoice to meet the terms of sale.

1. Determine the invoice date:
The invoice date can be assumed to be May 26, as it is the day the shipment arrived.

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

3. Determine the last day of the discount period:
To find the last day of the discount period, add the discount period of 10 days to the invoice date of May 26. This would be May 26 + 10 days = June 5.

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