In this section, “authority” means an authority as defined in § 12-101 of the Housing and Community Development Article. Subject to subsection (c) of this section, the property of an authority is not subject to property tax. An authority shall make a payment, if any, to the county and any municipal corporation that has a population of more than 1,000 in which any part of the exempt property is located in an amount determined by agreement with the county and the municipal corporation. The payment may not be greater than the property tax that would have been payable without this section. Notwithstanding § 7-104 of this title and after filing the application provided by § 7-103 of this title, property tax on any property that becomes exempt under this section is abated from the date during the taxable year when the instrument transferring title to the authority was recorded.