Until payment, or provision for payment, has been made of all principal, interest, and any other amounts owing on account of any outstanding long-term obligations, which are payable in whole or in part from taxes or assessments upon any property within all or any part of the territory of a dissolved district, the legislative body of the successor shall in each year provide for the levy and collection of taxes or assessments upon the property sufficient to pay any principal, interest, and any other amounts owing on account of such obligations, as they become due. Those taxes or assessments shall be levied and collected in the manner provided by the principal act of the dissolved district.