The City Council, at its first meeting in each fiscal year, shall designate one or more banks of approved and responsible standing in which the City Treasurer shall keep at all times all money held by him or her; provided, if more than one bank in the city meets the requirements for approved banks as herein defined, the said funds shall be deposited in each of them and the City Treasurer shall not give a preference to any one or more of them in the money he or she shall deposit. A bond shall be required from all banks so selected in a penal sum which equals the maximum amount on deposit at any time less the amount insured by the Federal Deposit Insurance Corporation or a pledge of sufficient assets of the bank to secure the payment of all such deposits.