The Board of Finance shall, in the month of June 1994, and not less frequently than once every three years thereafter, procure from chartered banks of known reliability and sufficient capital their offers to act as depositary for the City moneys, or for specified portions thereof, and the terms upon which they will receive such moneys, and also the terms upon which they will furnish money upon such temporary and emergency loans to the City, or specified portions thereof, as the City Council from time to time may authorize. They shall by vote determine which of said offers, if any, they accept, and appoint such bank or banks whose offer or offers are accepted, as depositary or depositaries of such moneys, or any portion thereof, to which any offer relates, as to them shall appear to be for the best interests of the City.