The Banking System

Expansion of Deposits

Expansion of deposits refers to the money created by fractional reserve banking, wherein money deposited in a bank is expanded by lending out a fraction of it.
Expansion of deposits is the process in which banks create additional money by using money already deposited. The money expands because when banks loan it out, it reenters the economy. In fact, most of the money supply in the United States is created in this fashion. Before being loaned out, deposits in a bank do not increase the overall money supply. The funds deposited merely change in composition from currency to deposit. Money is created only when funds that have been deposited are loaned out. Because banks are required to hold a fraction of deposits in reserve, only the remaining fraction, when lent out, increases the money supply. The fraction lent out is a multiple of the fraction that must be held in reserve. The mathematical function that describes the maximum possible expansion of deposits is known as the money multiplier. The money multiplier is the amount of money generated by the banking system with each dollar of reserves. It shows the total amount of money created by the system. The money multiplier is calculated with this equation:
Moneymultiplier=1Requiredreserveratio\mathrm{Money}\;\mathrm{multiplier}=\frac1{\mathrm{Required}\;\mathrm{reserve}\;\mathrm{ratio}}
The required reserve ratio (RR) is the percentage of deposits a bank is required to hold in reserve and not lend out or invest. For example, if a bank is required to reserve $1 for every $4 deposited, the required reserve ratio is 25%, or 0.25. The equation for arriving at the money multiplier would be 1/0.25=41\;/\;0.25\;=\;4 . Therefore, when the required reserve ratio is 0.25, the money multiplier is equal to 4.

The fraction of a deposit that a bank can loan out or invest is called excess reserves. It is through its excess reserves that a bank can grow its total reserves. For example, if a bank has $1 million in deposits and the required reserve ratio is 10%, the excess reserves for the bank is $900,000.

The process of deposit expansion does not end with that first bank loaning out its excess reserves because the borrower is likely to deposit the money in another bank for use in transactions. The second bank can use this deposit to expand the money supply again. For example, if an initial deposit made with Bank 1 is $100,000 and the required reserve ratio is 10%, the bank must hold 10% of $100,000 (or $10,000) in required reserves. This means Bank 1 has $90,000 in excess reserves, which it can lend out. If the bank lends out all $90,000 and $90,000 is deposited in Bank 2, which has the same required reserve ratio, then Bank 2 can lend out $81,000 of the deposited sum. If the maximum amount of money is lent out and deposited in Bank 3, this bank can lend out $72,900. In this way, starting from an initial deposit of $100,000, over the course of just three deposits, the money supply could potentially increase by $90,000+$81,000+$72,900=$243,900\$90,000+\$81,000+\$72,900=\$243,900 . This process continues on, so the total new money created is the value of the money multiplier times the initial deposit. In this example, the total new money created is 1 divided by 0.1, or 10 (money multiplier) times $100,000 (initial deposit), which equals $1,000,000. This continued expansion of the money supply that occurs when money created by fractional reserve banking is redeposited, which creates more money, which can itself be redeposited, and create further economic growth is called the multiple expansion of deposits.

Expansion of Deposits

New Deposits Required Reserves (10%) Excess Reserves
Initial deposit $100,000 $10,000 $90,000
Round 1 $90,000 $9,000 $81,000
Round 2 $81,000 $8,100 $72,900
Round 3 $72,900 $7,290 $65,610
Round 4 $65,610 $6,561 $59,049
Round 5 $59,049 $5,905 $53,144
Final impact on money supply $1,000,000 $100,000 $900,000

Initially, consumers deposit $100,000 in a bank. The bank has a required reserve ratio of 10 percent, so it places $10,000 in reserves and loans out the excess reserves of $90,000. With a required reserve ratio of 10 percent, the money multiplier is 1/0.10, which equals 10. Therefore, based on iterative rounds of lending, the final impact of this deposit is $900,000 ( $90,000×10=$900,000\$90,000\;\times\;10=\$900,000 ).