Enter Values
Key Formulas
Calculation Result
Formula Breakdown
Deposit Expansion by Round
| Round | New Deposit | New Lending | Currency Drain | Cumulative |
|---|
Model Assumptions
Key Assumptions
- Simple model: Banks lend all excess reserves; borrowers redeposit 100% in the banking system; no currency drain or voluntary excess reserves.
- Actual model: Accounts for excess reserves (e) and the currency-deposit ratio (c); borrowers and the public behave consistently each round.
- Does not model interbank lending, capital adequacy requirements (Basel III), or monetary policy transmission lags.
- Each round represents one complete lending cycle.
For educational purposes. Not financial advice. Market conventions simplified.
Understanding the Money Multiplier
What Is the Money Multiplier?
The money multiplier describes the maximum amount of money the banking system can create from a given amount of reserves. Through fractional reserve banking, an initial deposit ripples through the economy as banks lend out a portion of each deposit, which then becomes a new deposit at another bank. This process, known as deposit expansion, amplifies the initial deposit into a much larger total money supply.
Where rr = required reserve ratio
How Banks Create Money
When you deposit $100 and the reserve ratio is 10%, the bank keeps $10 as required reserves and lends $90. The borrower spends $90, and the recipient deposits it at another bank. That bank keeps $9 and lends $81. Each round creates progressively smaller new deposits, forming a geometric series. After many rounds, the total deposits converge to $1,000 — ten times the initial deposit.
Banks do not create physical currency. They create deposit money (checking accounts) through this lending process. The Federal Reserve controls the monetary base (currency + reserves), and the banking system multiplies it into a larger money supply.
Simple vs. Actual Model
The simple textbook model (m = 1/rr) assumes that all loans are fully redeposited. In reality, two leakages reduce the multiplier:
Excess Reserves (e)
Banks may hold reserves beyond the requirement for safety, especially during financial stress. After 2008, U.S. banks held trillions in excess reserves at the Fed, dramatically reducing the effective multiplier.
Currency Drain (c)
People hold cash instead of depositing all money. The currency-deposit ratio (c) measures how much cash the public holds relative to bank deposits. Higher cash preference means less money circulating through the banking system.
The March 2020 Reserve Requirement Change
On March 15, 2020, the Federal Reserve Board announced the reduction of reserve requirement ratios to zero percent, effective March 26, 2020. This was not a crisis measure but the formalization of a long-running shift: reserve requirements no longer played a significant role because the Fed had moved to an ample-reserves regime. The Fed now controls the money supply through interest on reserves (IOR), overnight reverse repurchase agreements, and other tools rather than reserve ratios.
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only. Results are based on simplified models from Mankiw's Principles of Macroeconomics (Chapter 16). Actual money creation involves additional complexities including capital requirements, lending standards, borrower behavior, and central bank policy tools. This tool should not be used for professional economic analysis or policy decisions.
