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rate of tax, or any ordinance lowering the rate or discontinuing the tax, shall be certified by the county clerk and filed with the Illinois Department of Revenue either (i) on or before the first day of April, whereupon the Department shall proceed to administer and enforce the tax as of the first day of July next following the filing; or (ii) on or before the first day of October, whereupon the Department shall proceed to administer and enforce the tax as of the first day of January next following the filing. Beginning January 1, 2014, the results of any election authorizing a proposition to impose a tax under this Section or effecting an increase in the rate of tax, along with the ordinance adopted to impose the tax or increase the rate of the tax, or any ordinance adopted to lower the rate or discontinue the tax, shall be certified by the county clerk and filed with the Illinois Department of Revenue either (i) on or before the first day of May, whereupon the Department shall proceed to administer and enforce the tax as of the first day of July next following the adoption and filing; or (ii) on or before the first day of October, whereupon the Department shall proceed to administer and enforce the tax as of the first day of January next following the adoption and filing. (g) When certifying the amount of a monthly disbursement to a county under this Section, the Department shall increase or decrease the amounts by an amount necessary to offset any miscalculation of previous disbursements. The offset amount SB3019 Enrolled LRB104 20255 HLH 33706 b Public Act 104-0468