Interest - When you close the transaction on your refinance, there will most likely be some outstanding interest due on the old loan.  For example, if you close on August twentieth (and you made your last payment), you will have twenty days interest due on the old loan and ten days prepaid interest on the new loan.  Your first payment on the new loan would not be until October 1st since you have already paid all of August's interest when you closed the refinance transaction (since interest is paid in arrears, a September payment would have paid August's interest, which has already been paid in closing).