There shall be a Police Pension Board consisting of five (5) members. Of these members, two (2) shall be appointed by the Mayor, serving a term of two (2) years each; two (2) shall be elected from the regular police force of the City, and one shall be elected from the beneficiaries of the pension. Each member shall serve for two (2) years and elected members shall be selected in the manner provided by statute. Provided, that the terms of the members of the Police Pension Fund first appointed shall commence on the second Tuesday of May following the adoption of this Chapter. (M.C. 1962, sec. 9.1401)