The obligations incurred by any city of the first class in the making of any such contracts shall not be considered as a part of its indebtedness under the provisions of its governing charter, or of any law of this state fixing the limit of amount of its indebtedness; nor shall it be required, at any time before making, or during the life of such contracts, to have specifically provided for the same by previous tax estimates or levy, or to provide for or have on hand in its treasury more money applicable to such contracts than the amount to be paid thereon during a single year.