The roads hereinbefore provided shall have been completed for a period of at least one month before the board of supervisors and the road commissioners shall finally accept the same and make final settlement therefor. Nor shall the board of supervisors allow any final payment to any contractor for the construction of any such road until an itemized statement shall be filed, showing in detail the amount that may be due for each separate mile, the number of yards hauled for each mile, and the amount of work completed for each mile.