Money Multiplier Calculator
Print| Maximum Potential Money Supply Expansion | $0.00 |
The Money Multiplier Calculator computes the maximum potential expansion of the total money supply generated by commercial banks through fractional reserve banking. The money multiplier demonstrates how an initial injection of central bank reserves (monetary base) expands into broader money supply (M1/M2) via sequential loan re-deposits.
Understanding the money multiplier helps macroeconomists and central bankers evaluate open market operations, set bank reserve requirements, and manage national liquidity.
Money Multiplier Formulas
The money multiplier can be calculated using a simple theoretical model or an empirical complex model:
1. Simple Fractional Reserve Money Multiplier
Simple Money Multiplier (m) = 1 / Reserve Requirement Ratio (r)
Total Money Supply Created ($) = Initial Excess Reserves × m
2. Complex Money Multiplier (With Currency Drain & Excess Reserves)
Complex Money Multiplier (m) = (1 + c) / (r + e + c)
Where:
- r (Required Reserve Ratio): Percentage of customer deposits that commercial banks must hold in reserve (as a decimal).
- c (Currency Drain Ratio): Ratio of physical currency held by the public to checkable bank deposits.
- e (Excess Reserve Ratio): Ratio of extra reserves held voluntarily by commercial banks above mandatory requirements.
Reserve Requirement & Deposit Expansion Matrix
The mandated reserve requirement ratio dictates maximum theoretical commercial credit expansion:
| Reserve Requirement Ratio (r) | Simple Multiplier (1 / r) | Total Money Created per $1,000 Reserve Deposit |
|---|---|---|
| 5% (r = 0.05) | 20.0x Multiplier | $1,000 initial deposit expands into up to $20,000 total broad money supply. |
| 10% (r = 0.10) | 10.0x Multiplier | $1,000 initial deposit expands into up to $10,000 total broad money supply. |
| 20% (r = 0.20) | 5.0x Multiplier | $1,000 initial deposit expands into up to $5,000 total broad money supply. |
| 100% (r = 1.00 – Full Reserve) | 1.0x Multiplier | $1,000 initial deposit creates zero extra credit. 100% full-reserve banking. |
Step-by-Step Money Multiplier Example
Suppose a central bank injects $1,000,000 into the banking system through open market bond purchases, with a 10% reserve requirement:
- Initial Excess Reserves Deposited: $1,000,000
- Mandatory Reserve Ratio (r): 10% (0.10)
Step 1: Compute Simple Money Multiplier
m = 1 / 0.10 = 10.0x
Step 2: Compute Maximum Potential Money Supply Created
Total Money Created = $1,000,000 × 10.0 = $10,000,000
Result: The initial $1,000,000 central bank reserve injection supports up to $10,000,000 in total bank checkable deposits across the commercial banking system.
Frequently Asked Questions (FAQ)
Why does the empirical money multiplier differ from the theoretical simple multiplier?
The simple multiplier assumes that banks lend out 100% of excess reserves and that the public holds zero cash currency. In reality, banks hold excess reserves (especially when central banks pay Interest on Reserve Balances / IORB) and the public holds cash, reducing the actual multiplier.
What happened to US reserve requirements in 2020?
In March 2020, the Federal Reserve reduced reserve requirement ratios to 0% for all depository institutions, shifting monetary control primarily to Interest on Reserve Balances (IORB) and repo rates.
What is the Currency Drain Effect?
The Currency Drain Effect occurs when bank loan recipients withdraw physical paper currency cash rather than keeping funds in checkable bank deposits. Physical cash withdrawals leak out of the banking system, lowering the money multiplier.
How does the Money Multiplier relate to Quantitative Easing (QE)?
During Quantitative Easing, central banks buy bonds to create massive bank reserves. If commercial banks choose to hold these as excess reserves rather than expanding loans, broad money multiplier rates collapse while monetary base (M0) surges.