The City Auditor shall keep in his office an account of all public improvements which are ordered by Council and are under contract, copies of which shall be furnished to him by the several departments authorized to make contracts on behalf of the City. The book shall show the estimate of the improvement, the amount certified to be paid for the improvement, the amount paid from time to time, and when any improvement is completed, the date of the final payment and the amount thereof. (1993 Code 31.43)