(4) Prior to the commencement of each fiscal year, the department of finance shall determine the total amount of taxes to be abated under this section with respect to each property for which rent exemption orders granted to persons sixty-two years of age or older were in effect for all or any part of the preceding calendar year. Prior to the commencement of each fiscal year, such agency as the mayor shall designate shall determine and, if such agency is not the department of finance, shall notify the department of finance of the total amount of taxes to be abated under this section with respect to each property for which rent exemption orders granted to persons with disabilities were in effect for all or any part of the preceding calendar year. The commissioner of finance shall make the appropriate adjustment in the real estate tax payable in such fiscal year.