At least once in each five-year period the actuary shall make an actuarial investigation into the mortality, service and compensation experience of the members and beneficiaries of the retirement system and shall make a valuation of the assets and liabilities of the system and taking into account the results of such investigation and valuation the board of trustees shall:
(1) Adopt for the retirement system such mortality, service and other tables as shall be deemed necessary;
(2) Certify the rates of contribution payable by the said cities.