Interest on mortgage loans is paid in arrears.  For example, when you make your June mortgage payment, a large portion of that payment covers the interest that built up during the previous month of May and the balance reduces the principal balance on the loan.  Since interest is usually paid in arrears, the seller will owe for that portion of the month he owns the property.  That is true whether the loan is assumed or paid off. 

When interest is prorated, the actual number of days for each month is used and either 360 or 365 days per year to calculate the interest cost per day.  The use of 360 or 365 days changes with lenders.  For the most conservative approach to estimate the amount of prorated interest owed by the seller, it is best to use the 360-day approach.