Whenever any person claiming the exemption from property tax under the provisions of subdivisions (59), (60), (70), (72), (74) and (76) of § 12-81 has failed to file a claim with the assessor or board of assessors as required in said subdivisions, the assessor or board of assessors, upon receipt of a request from such person, may allow an extension of time until the fifteenth day of December for the filing of such claim, provided whenever an extension of time is so allowed, such person shall be required to pay a fee for late filing to the municipality in which the property, with respect to which such claim is submitted, is situated, unless such fee is waived by the assessor or board of assessors. Said fee shall be calculated as follows: If the assessed value of the property with respect to which such claim is submitted is one hundred thousand dollars or less, said fee shall be fifty dollars; if the assessed value of the property with respect to which such claim is submitted is greater than one hundred thousand dollars but less than two hundred fifty thousand dollars, said fee shall be one hundred fifty dollars; if the assessed value of the property with respect to which such claim is submitted is equal to or greater than two hundred fifty thousand dollars but less than five hundred thousand dollars, said fee shall be two hundred fifty dollars; if the assessed value of the property with respect to which such claim is submitted is equal to or greater than five hundred thousand dollars, said fee shall be five hundred dollars. If any person is granted an extension of the November first date for filing a tax list in accordance with § 12-42, the date by which he shall be required to claim an exemption under subdivision (59), (60), (70), (72) or (74) of § 12-81 shall be automatically extended to the fifteenth day of December and such person shall not be required to request an extension of the filing date for such claim.