Consider there are 30 days in a given month.

Your box arrived at the warehouse on the 16th of the month. Instead of billing for the whole month, we bill for the rest of the month starting the day the boxes are processed.

30 - 16 = 14. 14 days are left in the 30 day month.

The monthly fee is $11 per box. Divide $11 by 30 days. 11/30 = .37 so 37 cents per day.

With 14 days left in the month, you are billed $.37 per day for the 14 days left in the month. @14* .37 = 5.13.

The prorated cost for the first month for a box that gets processed on the 16th is $5.13 per box.

* The first month is prorated only. The final month is not.

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