S.D. Codified Laws § 46A-11-31
At the time and place specified in a notice under § 46A-11-30, the board shall consider the petition. If the board determines that the petition is proper and required notice has been given, it has jurisdiction to hear and decide the matter. The board may adjourn the hearing from time to time. If the board determines that the facts stated in the petition are accurate, that an extension of time of payment of unpaid installments is necessary in order to prevent default in payment of a majority of assessments, and that the owners of property assessed for the project will benefit by an extension of unpaid installments, it may order that all or any portion of unpaid installments shall be extended for a period as it determines, not exceeding fifteen years from the date of the order. Interest on extended assessments is payable annually at the time provided in the original assessment.
SDCL 46A-11-31