The City Manager and the City Secretary and such other City officers and employees as the City Council may require, shall, before entering upon the duties of their offices, enter into a good and sufficient fidelity bond in a sum to be determined by the City Council, payable to the City of Freeport and conditioned upon the faithful discharge of the duties of such persons and upon the faithful accounting for all monies, credit, and things of value coming into the hands of such persons, and such bonds shall be signed as surety by some company authorized to do business under the laws of the State of Texas, and the premium on such bonds shall be paid by the City of Freeport, and such bonds must be acceptable to the City Council.