Answer: President Franklin D. Roosevelt, “Fireside Chat on Banking” (March 12, 1933)
First of all, let me state the simple fact that when you deposit money in a bank the bank does not put the money into a safe deposit vault. It invests your money in many different forms of credit—bonds, commercial paper, mortgages and many other kinds of loans. In other words, the bank puts your money to work to keep the wheels of industry and of agriculture turning around. A comparatively small part of the money you put into the bank is kept in currency—an amount which in normal times is wholly sufficient to cover the cash needs of the average citizen. In other words, the total amount of all the currency in the country is only a small fraction of the total deposits in all of the banks.
Source: Franklin D. Roosevelt: “Fireside Chat on Banking,” March 12, 1933. Online by Gerhard Peters and John T. Woolley, The American Presidency Project .
Resources on FDR at the Franklin D. Roosevelt Library and Museum