Payment for work done as a local improvement shall be made by warrant drawn on the Local Improvement Assessment Fund for the particular improvement created or to be created when assessments therefor are paid. Any warrant for a progress payment or final warrant drawn against a Local Improvement Assessment Fund, either to be created or already in existence, shall bear interest at the rate of 6 percent per year beginning on the 10th day after the date of the warrant. Total interest on such warrants shall not exceed the total amounts collected as interest from the properties assessed. When sufficient money is collected and is in the Local Improvement Assessment Fund to pay accrued interest on the oldest outstanding warrant and some portion or all of the principal on such warrant, the interest on the warrant shall cease as of the day when the principal amount or portion thereof is collected, to the extent of the amount collected.