Me. Rev. Stat. tit. 5, § 1555

The late fee shall apply to the period beginning on the day after the required payment date and ending on the date on which payment of the amount due on the invoice is made. An amount of a late fee which remains unpaid at the end of any 30-day period, after the required payment date, shall be added to the principal amount of the debt and, thereafter, late fees shall accrue on the added amount.