The City Secretary shall execute a bond, payable to the city, as required by law, conditioned that the City Secretary will faithfully perform the duties of the office. The City Council shall determine the amount of the bond at least annually. If the council fails to determine the amount of the bond for the succeeding year, the amount last prescribed shall continue to be the amount of bond required. Such bond shall be a corporate surety bond and the city shall pay all costs, premiums, and expenses connected therewith.