When you make a mortgage payment, you are paying interest that accrued during the previous month. So, your September 1st mortgage payment paid the interest that accrues from August 1 - 31.
When you payoff a mortgage, whether through refinancing or sale of the property, the lender will calculate and charge you interest from the first of the month through the day they receive the funds to pay your mortgage in full. So, if the funds arrive on September 9th, you will have to pay 9 days on interest.
However, for FHA loans, the borrower may be charged interest through the end of the month regardless of when the payoff funds actually get to the lender. So, even if your funds get to the lender at the 9th, you may still be required to pay interest for the remaining 21 days in September.
FHA says that they have allowed lenders to collect the full month of interest because holders of mortgage-backed securities expect a full month of interest regardless of when the loan is satisfied.
The Consumer Financial Protection Bureau (CFPB) has asked the FHA to review this policy because it can end up costing consumers hundreds of dollars in extra interest. FHA has agreed to change it's policy effective January 21, 2015.
For any housing or mortgage-related questions please contact me at BarkerLoans@gmail.com.