Payments on signed contracts shall be made in strict accordance with the terms of such contracts when the conditions laid down in such contracts have been faithfully complied with by the contractor. Invoices for partial payments on construction contracts shall bear the certificate of the City Engineer as to the percentage of completion of the contract at the date of the invoice and no payment shall be made of a greater proportion of the contract price than has been completed. Invoices against contracts shall be credited against outstanding encumbrances and charged against cash expenditures before they are paid. Checks for payment of invoices against contracts shall be prepared by the Director of Finance, and signed by him and the City Manager. Such checks shall be delivered promptly to the contractors.