## The Money Multiplier and a Multi-Bank System

In a system with multiple banks, the initial excess reserve amount that Singleton Bank decided to lend to Hank’s Auto Supply was deposited into Frist National Bank, which is free to loan out $8.1 million. If all banks loan out their excess reserves, the money supply will expand. In a multi-bank system, the amount of money that the system can create is found by using the money multiplier. The money multiplier tells us by how many times a loan will be “multiplied” as it is spent in the economy and then re-deposited in other banks.

Fortunately, a formula exists for calculating the total of these many rounds of lending in a banking system. The **money multiplier formula** is:

\(\cfrac{1}{\text{Reserve Requirement}}\)

The money multiplier is then multiplied by the change in excess reserves to determine the total amount of M1 money supply created in the banking system. See the Work it Out feature to walk through the multiplier calculation.

### Using the Money Multiplier Formula

Using the money multiplier for the example in this text:

Step 1. In the case of Singleton Bank, for whom the reserve requirement is 10% (or 0.10), the money multiplier is 1 divided by .10, which is equal to 10.

Step 2. We have identified that the excess reserves are $9 million, so, using the formula we can determine the total change in the M1 money supply:

\(\begin{array}{rcl}\text{Total Change in the M1 Money Supply}& =& \cfrac{1}{\text{Reserve Requirement}}×\text{Excess Requirement}\\ & =& \cfrac{1}{0.10}×$9\text{million}\\ & =& 10×$9\text{million}\\ & =& $90\text{million}\end{array}\)

Step 3. Thus, we can say that, in this example, the total quantity of money generated in this economy after all rounds of lending are completed will be $90 million.