The agreement between the commission and the municipality shall describe in detail all conditions which must be fulfilled to meet the applicable requirements of the federal Social Security Act, including a stipulation that the cost to the state of administering sections 7-452 to 7-459, inclusive, shall be paid by the municipalities and apportioned among them quarterly, by the commission, in the ratio which each municipality’s quarterly total payment to the system bears to the total payments of all municipalities made in the same quarter; and each municipality shall include in its annual budget a sum sufficient to meet the amount due as its contribution to the commission.