Any replenishment assessment levied pursuant to this article shall be due and payable to the district by each producer in quarterly installments on the last day for filing the statement of the production of ground water from the water-producing facility operated by such producer during the quarterly period required to be covered by such statement. The amount so due and payable shall be computed by multiplying the production in acre-feet of ground water so produced from such water-producing facility, as reported in such statement, by the rate of the replenishment assessment fixed and levied by the board for the fiscal year in which such production shall occur.