The City shall furnish all surety bonds for its officers, employees, appropriate board and commission members, and any other persons required by the Council to be bonded. The amount of such bonds shall, in each case, be fixed by the Council or all persons whose duties require that they handle or be concerned with the management of the money or other property of the City. These surety bonds shall be issued by a company authorized to do business in the State of Ohio, and the premium on such bonds shall be paid from the funds of the City.