The directors of all administrative departments whose duties include the handling of moneys, and all employees whose duties include the handling of moneys, belonging to the City of Longview, shall, before entering upon the duties of their office or employment, make bond in some responsible surety company authorized to do business in the state, acceptable to the City Council. Any such surety bond shall be conditioned that the principal thereon will faithfully perform and/or discharge the duties of his office, account for and pay over to the city all moneys and property coming into his hands belonging to the city, and if there are provisions of state law bearing upon the functions of his office under which the execution of a surety bond is required, it shall be further conditioned to comply therewith. Premiums for such surety bonds will be paid by the city.