An open-market purchase of $100 million by the Fed increases banks’ reserves by $100 million as the Fed credits their accounts with additional reserves. In other words, this open-market purchase increases the monetary base (currency in circulation plus bank reserves) by $100 million. Banks lend out the additional $100 million. Whoever borrows the money puts it back into the banking system in the form of deposits. Of these deposits, banks lend out $100 million × (1 − rr) = $100 million × 0.9 = $90 million. Whoever borrows the money deposits it back into the banking system. And banks lend out $90 million × 0.9 = $81 million, and so on. As a result, bank deposits increase by $100 million + $90 million + $81 million + . . . = $100 million/rr = $100 million/0.1 = $1,000 million = $1 billion. Since in this simplified example all money lent out is deposited back into the banking system, there is no increase of currency in circulation, so the increase in bank deposits is equal to the increase in the money supply. In other words, the money supply increases by $1 billion. This is greater than the increase in the monetary base by a factor of 10: in this simplified model in which deposits are the only component of the money supply and in which banks hold no excess reserves, the money multiplier is 1/rr = 10.