Whenever the United States, the state, or a city, town, county, school district, or any other political subdivision, including, but not limited to, a turnpike authority, municipal trust, water or conservation district, flood control district, levee or waterway improvement district, urban renewal authority, public housing authority, or any other authority authorized by law, state or federal, acquires title to any real property for a governmental purpose between January 1 and October 1 of the tax year, such property shall be relieved of ad valorem tax for the remaining months of the year beginning with the first of the month next succeeding the date its acquisition for public purposes becomes a matter of public record, if the deed thereto was recorded prior to October 1; provided, however, that all taxes assessed against such property prior to its acquisition shall be paid in full and there be paid a sum equal to one-twelfth ( ¹/₁₂ ) times the number of months that the property remained in private ownership of an amount estimated by the county treasurer of the county wherein the real property lies to be substantially equal to the amount of tax which would have been or will become due and payable for the year had the real property not been acquired for public purposes. In estimating the amount of taxes which would have been or will become due and payable for the tax year had the real property not been acquired for public purposes the county treasurer shall use as a basis the current assessment and the tax rate for the preceding year, unless the tax for the current year shall be by then determined and set, in which event he shall use as basis the new assessment and rate. The public agency acquiring the property shall deduct the amount of such taxes from the purchase price payable to the private owner and remit the same to the county treasurer in satisfaction of such taxes. The county treasurer of any county is hereby authorized upon order of the board of tax roll corrections to cancel of record all taxes assessed against such property for the year of its acquisition when the deed thereto was recorded prior to October 1 and the aforesaid estimated amount of the tax for the months that the property was in private ownership is paid, which order shall be issued upon application of the acquiring authority.