As a result of there being no mortgage payment due the first month following your closing; at the closing you must pay simple interest covering the period from the day of the closing through the end of the month.
A calculation will be done at the closing to determine the amount of money that will need to be initially deposited to your escrow account. The actual amount will depend on the dollar amount and timing of the first tax payment coming due. The bank will need to make certain that there will be sufficient funds on account to make this first payment. Generally speaking, you can expect this amount to range anywhere from 4 to 6 months worth of payments.