The governing body of any city may authorize and provide for a delay in the payment following a financial analysis of special assessments for the cost of constructing public improvements in unplatted and undeveloped areas of the city. The governing body of such city may provide for a delay in the commencement of payment of some or all special assessments upon such property for a designated period of not to exceed 15 years or until such property is platted or developed if the same occurs prior to the conclusion of the period designated. In the event a benefit district is not developed to 50% of its area, an additional extension of 10 years before commencement of payments may be granted in the benefit district. All such assessments shall be due and payable at the time such property is platted or developed or at the expiration of the designated period. The payments for land which has not been platted or developed within the extension period shall become due and payable in a like manner as if the time for the payment of special assessments had not been delayed and extended.