In the year 1933 and at least once in each five-year period thereafter 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 funds 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 members under the provisions of sections 86.010 to 86.193; and
(3) Certify the rates of contribution payable by the said cities in accordance with section 86.153.