The Money Multiplier: How Banks Create Money

The money multiplier is the factor by which the banking system expands an initial deposit into a larger total money supply, and its formula is simply 1 divided by the reserve ratio. If banks must hold 10% of deposits in reserve, the money multiplier is 1 / 0.10 = 10, meaning a single $1,000 cash deposit can support up to $10,000 in total deposits once it works its way through the banking system, of which $9,000 is newly created money. This sounds like magic, but it is just the arithmetic of fractional reserve banking: banks keep only a fraction of deposits on hand and lend the rest, and those loans become new deposits at other banks, which lend again. This guide walks through the formula, the deposit-expansion chain with real numbers, and the reasons the real-world multiplier is smaller than the textbook one.

The formula

The simple money multiplier is:

Money multiplier = 1 / reserve ratio

The reserve ratio (also called the required reserve ratio or reserve requirement) is the fraction of deposits banks must keep rather than lend. Written as a decimal, a 10% requirement is 0.10, a 20% requirement is 0.20, and so on. The maximum expansion from an injection of new reserves is:

Maximum expansion = Initial deposit x Money multiplier

One subtlety in what this expansion means. When the initial $1,000 is cash the public already held, depositing it lifts total deposits to $10,000 but raises the money supply by only $9,000, the deposit times (multiplier − 1), because the currency in circulation fell by the $1,000 that got deposited. When the central bank instead injects brand-new reserves by buying bonds, no offsetting currency disappears, so the money supply rises by the full injection times the multiplier.

The smaller the reserve ratio, the more banks can lend from each deposit, and the larger the multiplier. A 20% ratio gives a multiplier of 1 / 0.20 = 5; a 10% ratio doubles that to 10; a 5% ratio gives 20. You can check any of these on the money multiplier calculator, and the full calculate hub has the related tools for the spending multiplier and other macro formulas.

How banks create money: the deposit chain

Banks create money not by printing it but by lending. Here is the mechanism, step by step, with a 10% reserve ratio and an initial $1,000 cash deposit.

Round 1. You deposit $1,000 in Bank A. Bank A must keep 10%, so it holds $100 in reserve and lends out the other $900. That $900 goes to a borrower who spends it.

Round 2. The person who received the $900 deposits it in Bank B. Bank B keeps 10% ($90) and lends $810.

Round 3. That $810 is deposited in Bank C, which keeps $81 and lends $729.

This continues, each round smaller than the last because a slice leaks into required reserves every time. Adding up all the deposits created across infinitely many rounds gives a geometric series:

$1,000 + $900 + $810 + $729 + ... = $1,000 x (1 / 0.10) = $10,000

The original $1,000 has supported $10,000 in total deposits. Of that, $9,000 is newly created money in the form of loans; the remaining $1,000 is the original cash. So while total deposits reach $10,000, the money supply itself grows by $9,000, because the $1,000 that started the chain was already currency in circulation before it was deposited. This is why economists say banks create money: no printing press is involved, just the repeated lending of deposits under a fractional reserve rule. For a fuller narrative of this process, see our companion guide on how banks create money.

A second worked example

Change the reserve ratio and watch the multiplier change. Suppose the central bank buys $5,000 of bonds from a bank, injecting $5,000 of new reserves, and the reserve ratio is 20%. Because this is a fresh reserve injection rather than a deposit of existing cash, the whole expansion counts as new money.

Money multiplier = 1 / 0.20 = 5

Maximum change in money supply = $5,000 x 5 = $25,000

Now suppose the central bank wants a larger effect and the reserve ratio is lowered to 12.5%:

Money multiplier = 1 / 0.125 = 8

Maximum change = $5,000 x 8 = $40,000

A lower reserve requirement gives banks more room to lend, so the same reserve injection creates more money. This is exactly why the reserve requirement is one of a central bank's monetary policy tools, alongside open market operations and the discount rate.

Why the real multiplier is smaller

The formula above gives the maximum possible expansion, and it assumes two things that rarely hold perfectly in practice. Two leakages shrink the real-world multiplier:

• Currency drain. The simple model assumes every loan is fully redeposited into a bank. In reality people hold some of the money as cash in their wallets. Any money held outside banks cannot be lent again, so it drops out of the multiplication.
• Excess reserves. The model assumes banks lend every dollar they are not required to hold. But banks often keep excess reserves, reserves above the requirement, especially when lending looks risky or interest rates on reserves are attractive. Reserves held voluntarily are not lent, so they too cut the multiplier.

Because of these leakages, the actual money multiplier is usually well below 1 / reserve ratio. When both leakages are large, as they were after 2008 when banks piled up excess reserves, the effective multiplier can fall dramatically, which is one reason large increases in bank reserves did not translate into proportionally large increases in the money supply or in lending.

The multiplier in the modern era

The simple 1 / reserve ratio story assumes the reserve requirement is the binding constraint on how much banks lend. Since the 2008 financial crisis, that assumption has largely broken down in the United States, for two reasons.

First, the Federal Reserve began paying interest on reserves in 2008. When banks earn a safe, risk-free return just for parking money at the central bank, holding excess reserves is no longer costly, so they hold enormous quantities of them. The banking system shifted from scarce reserves, where every spare dollar was lent out, to abundant reserves, where trillions sit idle. In that world the deposit-expansion chain never runs to completion, and the effective multiplier stays far below the textbook figure.

Second, in March 2020 the Fed cut the required reserve ratio to zero. With no reserve requirement at all, the expression 1 / reserve ratio is not even defined, and the mechanical multiplier no longer describes how the money supply is set. Modern central banks instead steer the economy by adjusting the interest rate they pay on reserves and the rate they target in money markets, not by rationing a fixed quantity of reserves.

None of this makes the money multiplier useless. It is still the cleanest way to see how fractional reserve banking turns one deposit into a chain of loans, and it is still the model AP and IB exams test. Just read it as a ceiling on money creation under a scarce-reserves regime rather than a literal account of how the money supply is determined today.

Why it matters

The money multiplier is the link between the reserves a central bank controls and the broader money supply that actually circulates. When the central bank wants to expand the money supply, it adds reserves (by buying bonds) and relies on the multiplier to turn a modest reserve injection into a larger change in deposits and loans. When it wants to contract, it drains reserves and the process runs in reverse. Understanding the multiplier is therefore essential to understanding how monetary policy transmits from the central bank to the real economy.

For exam purposes, expect two kinds of questions. The first is direct calculation: given a reserve ratio and an initial deposit or reserve injection, compute the multiplier and the maximum change in the money supply. The second is conceptual: explain why the actual expansion falls short of the maximum, which is where currency drain and excess reserves come in. Practice the arithmetic on the money multiplier calculator, read the process narrative in how banks create money, and lock in the vocabulary, required reserve ratio, fractional reserve banking, and excess reserves, through the glossary. Once the deposit chain clicks, the whole money-creation story becomes just a geometric series you can reproduce from memory.