In cities of the second class and villages, for all paving and improvements of the intersections and areas formed by the crossing of streets, avenues, or alleys, and one-half of the streets adjacent to real estate owned by the United States, the State of Nebraska, or the city or village, the assessment shall be made upon all of the taxable property of such city or village; and for the payment of such paving or improvements the mayor and city council or the village board of trustees are hereby authorized to issue paving bonds of the city or village, in such denominations as they deem proper to be called Intersection Paving Bonds payable in not to exceed fifteen years from the date of such bonds, and to bear interest payable annually or semiannually. Such bonds shall not be issued until the work is completed and then not in excess of the cost of such improvements. For the purpose of making partial payments as the work progresses in paving, repaving, macadamizing or graveling, curbing, and guttering or improvements of streets, avenues, alleys, or intersections and areas formed by the crossing of streets, avenues, or alleys, or one-half of the streets adjacent to real estate owned by the United States, the State of Nebraska, or the city or village, warrants may be issued by the mayor and city council, or the village board of trustees, upon certificates of the engineer in charge showing the amount of the work completed and materials necessarily purchased and delivered for the orderly and proper continuation of the project, in a sum not exceeding ninety-five percent of the cost thereof, and upon completion and acceptance of the work issue a final warrant for the balance of the amount due the contractor, which warrants shall be redeemed and paid upon the sale of bonds authorized by law. The city or village shall pay to the contractor interest, at the rate of eight percent per annum on the amounts due on partial and final payments, beginning forty-five days after the certification of the amounts due by the engineer in charge and approval by the governing body and running until the date that the warrant is tendered to the contractor. Nothing in this section shall be construed as authorizing the mayor and city council or village board of trustees to pave or gravel any intersections or areas formed by the crossing of streets, avenues, or alleys unless in connection with one or more blocks of street paving or graveling of which the paving or graveling of such intersection or area shall form a part.