The superintendent in charge of construction shall make monthly estimates of the amount of work done and furnish one copy to the contractor and file the other with the secretary of the board of drainage commissioners and the board shall meet and direct the secretary to draw a warrant in favor of such contractor for ninety per cent of the work done, according to the specifications and contract. Upon the presentation of such warrant properly signed by the chairman and secretary to the treasurer of the drainage fund he shall pay the amount due thereon. When the work is fully completed and accepted by the superintendent he shall make an estimate for the whole amount due, including the amounts withheld on the previous monthly estimates, which shall be paid from the drainage fund as before provided.