The deposit expansion multiplier is the multiplicative factor by which the money supply will grow in proportion to its base of physical currency, as a result of loans made in a fractional reserve monetary system. It is equal to:

1 / required reserve ratio

Banks must hold an amount of physical currency equal to the portion of their checking deposits represented by the required reserve ratio. In other words, if the required reserve ratio is 10%, a bank must hold one tenth of its demand deposits (money deposited into checking accounts) in the form of physical currency. The rest may be loaned out, at interest. This is how banks make profits.

If the amount of physical currency in circulation is represented by M0, then the money supply can grow to:

M0 * (1 / required reserve ratio)

If the required reserve ratio is 10%, then the deposit expansion multiplier is 10, which means that the money supply can grow to 10 times the amount of physical currency in circulation.