In a city of the first class, for all 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, the assessment shall be made upon all the taxable property of the city, and for the payment of such improvements, the mayor and city council are hereby authorized to issue improvement bonds of the city in such denominations as they deem proper, to be called Intersection Improvement Bonds, payable in not to exceed twenty years from date of the bonds and to bear interest payable annually or semiannually. Such bonds shall not be issued in excess of the cost of such improvements. For the purpose of making partial payments as the work progresses in making the 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, warrants may be issued by the mayor and city council 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 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 city council, 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 to make improvements of any intersections or areas formed by the crossing of streets, avenues, or alleys, unless in connection with one or more blocks of any of aforesaid kinds or forms of street improvement of which the improvement of such intersection or areas shall form a part.