Within the Department of Finance, there shall be a City Treasurer; provided that the Finance Director shall be ex-officio City Treasurer except when the Council by ordinance provides that the City Administrator shall appoint a City Treasurer for an indefinite term. Subject to such regulation as the Council may prescribe, the City Treasurer shall deposit funds received for the City in such depositories as the Council may designate. The City Treasurer shall have such other powers, duties, and functions as may be prescribed by the Charter, by applicable law, or by ordinance.