How banks create money, round by round
Deposit $1,000 at a bank and the money does not sit in a vault with your name on it. The bank holds a fraction in reserve and lends the rest to someone else — who spends it, so it lands as a deposit at another bank, which holds its fraction and lends the rest again. Each round creates a brand-new deposit that did not exist before, which is why economists say banks create money. The chain cannot run forever: every round, the required reserve nibbles away at what can be re-lent, and the deposits shrink geometrically toward zero. The money multiplier is the sum of that whole series — the ceiling on how much money one new deposit can support. The formal model dates to Chester Phillips's Bank Credit (1920) and has anchored money-and-banking courses ever since.
The formulas
Simple: m = 1 ÷ rr
With leakages: m = (1 + c) ÷ (c + r + e)
Maximum money = initial deposit × m
where rr (or r) is the required reserve ratio,c the currency-drain ratio (cash the public holds per dollar of deposits), and e the excess-reserve ratio, all as decimals. Set c = e = 0 and the fuller formula collapses to the simple one. Because c and e only add to the denominator faster than the numerator, real-world multipliers are always smaller than 1 ÷ rr.
Worked example
Take the canonical classroom case: a $1,000 deposit into a banking system with a 10% required reserve ratio. Watch the chain shrink and sum:
| Step | Amount |
|---|---|
| Round 1 — the first bankreceives $1,000, holds 10% ($100) in reserve, lends the rest | lends $900 |
| Round 2 — the loan is redepositeda second bank receives $900, reserves $90, lends the rest | lends $810 |
| Round 3 — and againa third bank receives $810, reserves $81, lends the rest | lends $729 |
| Multiplier = 1 ÷ 10%the geometric series of shrinking deposits sums to this multiple | 10× |
| New loans and deposits created along the wayeverything beyond the original $1,000 | $9,000 |
| = Maximum money supported by the $1,000 deposit$1,000 × 10 | $10,000 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, including the full five-round table, then swap in your own ratio and deposit.
From the blackboard to the real world
The simple multiplier is a ceiling, and the real world falls short of it for predictable reasons. People hold part of every loan as cash (currency drain), banks keep buffers above any requirement (excess reserves), and lending only happens when someone creditworthy wants to borrow. The "with leakages" mode prices in the first two, and the effect is dramatic: adding a 10% currency drain and 5% excess reserves to a 10% reserve ratio cuts the multiplier from 10 down to 4.4. Then came the deeper change — after 2008 the Fed flooded the system with reserves, and in March 2020 it dropped reserve requirements to zero outright. In the ample-reserves era, the binding constraints on bank lending are capital rules and loan demand, and the Fed's lever is the interest rate it pays on reserves. The multiplier survives as what it always was at heart: the cleanest way to see that lending creates deposits.
The same round-by-round logic drives fiscal policy'sspending multiplier, where re-spending rather than re-lending does the multiplying. And two neighbors on the money side: see what money growth means for prices with theinflation calculator, or how deposits grow for the saver holding them with thecompound interest calculator.
Frequently asked questions
What is the money multiplier?
The money multiplier is the maximum amount of money the banking system can create per dollar of new reserves under fractional-reserve banking. When you deposit cash, your bank keeps a fraction in reserve and lends the rest; the loan is spent and redeposited at another bank, which repeats the split. The multiplier — 1 divided by the reserve ratio in the simple model — is the total money supply that chain can support at its limit. With a 10% reserve ratio, one new dollar of deposits can support up to ten dollars of money.
Why does the multiplier equal 1 divided by the reserve ratio?
Because the lending rounds form a geometric series. With a 10% reserve ratio, a $1,000 deposit produces a $900 loan, then an $810 loan, then $729, each round 90% of the last. The sum of the series 1,000 × (1 + 0.9 + 0.9² + …) is 1,000 ÷ (1 − 0.9) = 1,000 ÷ 0.10 = $10,000. In general the series sums to the initial deposit divided by the reserve ratio, which is why the multiplier is exactly 1 ÷ rr.
What stops money creation in practice?
Three leakages shrink the multiplier below its theoretical maximum. First, currency drain: people hold some of each loan as cash instead of redepositing it, pulling money out of the chain. Second, excess reserves: banks often hold more reserves than required, especially in uncertain times. Third, loan demand: banks cannot lend if creditworthy borrowers do not want to borrow. The fuller formula, m = (1 + c) ÷ (c + r + e), captures the first two — switch this calculator to "with leakages" mode to see how much they matter.
Is the money multiplier model still accurate today?
Not as a description of modern US policy. The Federal Reserve reduced reserve requirement ratios to 0% effective March 26, 2020, and now operates an "ample-reserves" regime in which it steers the economy by setting the interest rate paid on reserves rather than by rationing their quantity. Banks today are constrained by capital rules, liquidity regulation, and loan demand — not a required reserve ratio. The multiplier remains the standard textbook model for understanding how fractional-reserve banking creates deposits, and it still appears on economics exams.
What are M1 and M2?
They are the two money-supply measures the multiplier expands: M1 is the most liquid money — currency in circulation plus checkable and other liquid deposits — while M2 adds slightly less liquid savings vehicles such as small time deposits and retail money-market funds. When this calculator says a $1,000 deposit can support $10,000 of money, that new money shows up as deposits, the largest component of M1. The Federal Reserve publishes both aggregates monthly in its H.6 statistical release.
Sources
- OpenStax, Principles of Economics 3e — How Banks Create Money
- Federal Reserve Board — Reserve Requirements (ratios set to 0% effective March 26, 2020)
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Disclaimer: This calculator is foreducation and illustration only. It computes the textbook fractional-reserve model, which shows a theoretical maximum — actual money creation depends on currency holdings, bank behavior, regulation, and loan demand, and US reserve requirements have been 0% since March 2020. Nothing here is investment, banking, or policy advice.