Whenever any portion of the cost of a public improvement shall be assumed by or charged to the City at large and the balance of such cost assessed to the property benefited, if the Council shall provide for the payment of the City's portion of such cost in installments, then in such case bonds may be issued in anticipation of the payment of the amount assessed to the City-at-large, the same as they may be issued in anticipation of the payment of the amount assessed to the benefited property. In such case, there shall be appropriated each year an amount sufficient to pay the bonds issued in anticipation of the collection of assessments against the City, when the same fall due. Nothing in this section contained shall be construed to require the financing of the City's portion of the cost of any improvement in the manner herein specified. It shall not be necessary to issue a separate series of bonds for the City's portion of the cost of any such public improvement but such bonds may be included as a part of a total issue against all special assessments, including those against the City.