There shall be a Board of Zoning Appeals composed of five (5) electors, appointed by the Mayor with the approval of Council. Their terms shall begin on January 1 next following the adoption of this Charter. One shall be appointed for a term of five (5) years, one for a term of four (4) years, one a term of three (3) years, one for a term of two (2) years, and one for a term of one (1) year. At expiration of the term of each member further appointments shall be for terms of five years. Vacancies in the board shall be filled in the same manner as original appointments but shall be the balance of the term only.