From what I understand, banks prefer to have loan payments due on the 1st of the month. To that end, if you close on a property on, say, the 15th, they will charge you a pro-rated payment to get you to the 1st of the next month, after which you make your payments as planned.
1) How does the pro-rated payment get calculated in terms of how much goes to interest and how much to principal?
Also, 2) are the rest of the payments (from the 1st of the next month) calculated as if the principal was the original minus the principal paid in the one pro-rated payment?
Example for #2 - say you close on the January 15th for a $100,000 loan. Pretend pro-rated is $300 principal, $300 interest. Would you calculate the rest of the payments, starting on February 1st, as if you have a completely new loan with principal of $99,700?