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'll follow these steps:

Step 1: Calculate the net amount payable
The net amount payable is the total amount of the merchandise minus any returns and any eligible cash discounts. In this case:
Total amount of merchandise = $17,700
Shipping charges = $550
Damaged carpet return value = $1,390

Net amount payable = (Total amount of merchandise + Shipping charges) - Damaged carpet return value
Net amount payable = ($17,700 + $550) - $1,390
Net amount payable = $18,250 - $1,390
Net amount payable = $16,860

Step 2: Calculate the discount period
The terms of sale state "2/10, n30 ROG". This means that the customer can take a 2% discount if they pay within 10 days, otherwise, the full amount is due within 30 days from the "receipt of goods" (ROG) date.

The shipment arrives on May 26. We need to count 10 days from this date to determine the end of the discount period.
May 26 + 10 days = June 5

Step 3: Determine the payment due date
To find the payment due date, we add the number of days from the discount period (10 days) to the date when the discount period ends (June 5).

Payment due date = Discount period end date + Number of days from the discount period
Payment due date = June 5 + 10 days
Payment due date = June 15

So, Empire Carpet Company must pay the invoice by June 15 to take advantage of the cash discount.