When you buy a new home, your first mortgage payment is due on the first day of the month after the first full month that you own the home. For example, if you close the sale of your new home on April 25, the first full month you spend in the home will be May, so your first payment will be due on June 1.
The timing of your first mortgage payment demonstrates a key difference between the structure of mortgage payments and rent payments. Renters usually pay in advance: The money you pay on April 1 is for occupancy in the month of April, the money you pay on May 1 is for May, and so forth. Mortgages, by contrast, are "paid in arrears." This means that you pay for occupancy in the month just completed. In other words, a mortgage payment that's due on May 1 covers occupancy for April.
You may be wondering why you don't have to make a mortgage payment on the first day of the month immediately after you buy the house. For example, if you close the sale on April 25, why there isn't a payment due on May 1 that covers April 25 to April 30? The answer has to do with "amortisation," which is the way your lender calculates your payment. In an amortised mortgage, every payment covers a full month, and every payment is for the same amount. The formulas that lenders use to amortise mortgages only work with whole months (e.g., 360 months for a 30-year loan, or 180 months for a 15-year loan). They can't account for extra days between the closing date and the first day of the next month.
Per Diem Interest
Although you don't have a mortgage payment due on May 1 in the previous example, this doesn't mean you get to live in the house for free from April 25 to April 30. Your lender still charges you interest for those days, at a daily rate based on the amount and interest rate of your mortgage loan. This is "per diem" interest, and you pay it upfront at the closing.
Depending on when you close the sale, per diem interest can add hundreds of dollars to your closing costs. For this reason, many homebuyers try to schedule the closing date as close to the end of the month as possible; having fewer days left at the end of the month means less money in per diem interest.