Whenever an order, under section 414.031, 414.0325, or 414.033, annexes part or all of a township to a municipality, the order may provide that the tax rate of the annexing municipality on the area annexed shall be increased in substantially equal proportions over not more than six years to equality with the tax rate on the property already within the municipality. The appropriate period, if any, shall be based on the time reasonably required to effectively provide full municipal services to the annexed area.