Prorated Interest
When receiving multiple payments, for accounting purposes, it is easier to have all payments coming in on the same day (a tool also used by landlords). For this reason at closing lenders will prorate the interest from the date of the closing to the 1st of the following month. On the 1st the interest starts accruing as usual, and the next payment is due on the 1st of the month after that.
For example, if the closing takes place on the 20th of March, interest will be prorated 12 days to the 1st of April. On the closing statement will be a charge for 12 days of interest x the daily $ rate. The next payment due will be the regular monthly payment due on May 1st.