The administration of the retirement system is hereby vested in the board of administration created in RCW 41.28.080. The board shall exercise the powers and duties conferred upon it by said section, and in addition thereto:

(1) The board shall keep in convenient form such data as shall be necessary for the actuarial valuation of the retirement fund created by this chapter. At the end of the five-year period beginning with the year 1939, and at the end of every five-year period thereafter, the board shall cause to be made an actuarial investigation into the mortality, service and compensation experience of the members, and beneficiaries as defined by this chapter; and shall further cause to be made an actuarial valuation of the assets and liabilities of the retirement fund, and upon the basis of such investigation and valuation and subject to the approval of the city council or city commission, shall:

(a) Make any necessary changes in the rate of interest;

(b) Adopt for the retirement system such mortality, service and other tables as shall be necessary;

(c) Revise or change the rates of contribution by members on the basis of such mortality, service and other tables.

(2) The board shall promptly transmit to the city council or city commission a report covering the actuarial investigation and actuarial valuation provided for in subdivision (1) of this section.

(3) In addition to other records and accounts, the board shall keep such detailed reports and accounts as shall be necessary to show the financial condition of the retirement fund at all times.

(4) The board shall annually transmit to the city council or city commission a report showing the financial condition of the fund established by this chapter.