(a) When application is made for a permit to operate any hotel after January 1 of any year, the fee charged for the permit shall be one-half (½) the annual rate.
(b) When application is made for a permit to operate any public swimming pool after October 1 of any year, the fee charged for the permit shall be one-half (½) the annual rate.
(c) When the hotel was subject to permit requirements prior to January 1 of any year, or where the public swimming pool was subject to permit requirements prior to April 1 of any year, no such fractional rate shall be allowed.