To pay the cost of the improvement as the work progresses the county may issue progress warrants drawn against the rural road improvement fund for the total cost of materials purchased on receipt of the materials, for the right-of-way acquired, for engineering and legal expense, and other incidental expenses, and ninety-five percent of the cost of the work completed and materials necessarily purchased and delivered for the orderly and proper continuation of the project by the contractor as certified by the engineer in charge. On completion of the contract and the acceptance of the improvement by the county, a warrant may be drawn for the balance due the contractor. The warrants shall draw interest at the rate set by the county board. The county shall pay to the contractor interest, at the rate of eight percent per annum on the amounts due on partial and final payments, beginning forty-five days after the certification of the amounts due by the engineer in charge and approval by the governing body and running until the date that the warrant is tendered to the contractor.