Most lenders based the date of the first payment on the closing date.  If the closing occurs on the first day of the month, the first payment will be due on the first day of the following month.  If the loan closes on any day other than the first day of the month, the lender will usually require a payment at closing for the period from and including the day of closing up to an including the last day of that month.  That payment is referred to as an “interest adjustment”.  In this case, the first mortgage payment is due the first day of the second month following the day of closing.  The purpose of the interest adjustment is to allow the buyer’s monthly payment to come due the first day of each month.