The board of trustees shall elect from its membership a chairman and shall, by majority vote of its members, appoint a secretary, who may be, but need not be one of its members. It shall engage such actuarial and other services as shall be required to transact the business of the retirement system. The compensation of all persons engaged by the board of trustees and all other expenses of the board necessary for the operation of the retirement system shall be paid at such rates and in such amounts as the board of trustees shall approve.