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ECONOMICS • MONEY & BANKING

Money Multiplier & Reserve Banking

Follow a deposit through repeated reserve and lending rounds to see how reserve requirements and cash leakage change deposit expansion.

● DEPOSIT CASCADEReserves → loans → redeposits
Deposits shown
Loans shown
Long-run multiplier
Redeposit rate

Reasoning inspector

live model state
Reserve ratio—
Currency drain—
Redeposit fraction—
Long-run multiplier—
Deposits after rounds—
Loans after rounds—
Next redeposit—

Experiment with the mechanism

The textbook multiplier is a geometric process, not money appearing from nowhere. Each lending round is smaller because reserves and currency leakage remove funds from the next redeposit.

LEARN WITH THE SIMULATION

Understand Money Multiplier & Reserve Banking by experimenting.

START HERE

The textbook money multiplier can be represented as a sequence of deposits, required reserves, loans and redeposits. Each round is smaller because banks hold reserves and some funds may leak into currency rather than returning to deposits.

BUILD THE IDEA

What you should understand first

  • Trace how a deposit can support repeated lending and redeposit rounds.
  • Explain how a higher reserve ratio reduces the geometric multiplier.
  • See how currency leakage shrinks deposit creation even when reserve rules are unchanged.

TRY IT YOURSELF

Which reduces deposit expansion more: a higher reserve ratio or more currency drain?

  1. Play through the default lending rounds and record the long-run multiplier.
  2. Raise the reserve ratio while holding currency drain fixed.
  3. Reset, restore the reserve ratio, and instead raise currency drain.
  4. Compare the redeposit fraction and total deposits.
Read the visual:

Both reserve requirements and cash leakage reduce the fraction that reaches the next deposit round. The multiplier falls as either leakage grows.

WHY IT WORKS 01

The multiplier is a geometric series

The multiplier follows a geometric series because each round is a constant fraction of the previous deposit. If the initial deposit is D and the redeposit fraction is r, the sequence is D, Dr, Dr² and so on. As long as |r| is below one, the rounds shrink and the theoretical long-run sum approaches D/(1-r), which is why small changes in r can produce large changes in the final total.

WHY IT WORKS 02

Leakages compound together

Reserve retention and currency drain are separate leakages, but they combine multiplicatively in the next-round fraction: r = (1 − reserve ratio)(1 − currency drain). Raising either leakage makes each successive bar shrink faster. The model therefore distinguishes the size of the initial deposit, which scales the whole cascade, from the multiplier itself, which is controlled by the fraction that survives into the next round.

DO NOT MIX THESE UP

Common misconception

The multiplier is not a promise that banks mechanically create the maximum possible deposits, and it is not a literal description of modern monetary policy. Loan demand, bank capital, regulation, settlement systems and central-bank operations matter in reality.

PRACTICE CHALLENGE

Can you cut the long-run multiplier roughly in half without changing the initial deposit?

  • Record the default long-run multiplier.
  • Change only the reserve ratio or only currency drain.
  • Use Play to inspect how quickly rounds shrink.
  • Find settings that reduce the multiplier by about half and explain why.
Reveal the reasoning

Yes. The multiplier is 1/(1-r), where r is the redeposit fraction. Lowering r enough raises the denominator and reduces the long-run sum; the initial deposit only scales the level, not the multiplier itself.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Banks hold a fixed reserve fraction of each deposit and lend the remainder.
  • A fixed fraction of every loan is redeposited while the rest leaks into currency.
  • The sequence uses a geometric cascade with no capital constraint, default, interest rate or loan-demand limit.

Model limitations

  • Modern banking systems are not mechanically constrained by a simple reserve multiplier in the way this classroom model suggests.
  • Central-bank policy, bank capital, liquidity regulation, settlement balances and endogenous credit demand are omitted.

CONNECT IT

Where this matters

  • Introductory money and banking
  • Reserve-ratio intuition
  • Geometric-series applications
  • Understanding leakage in repeated spending flows

WORDS THAT MATTER

Key vocabulary

Reserve ratio
The fraction of a deposit held as reserves in this simplified model.
Currency drain
The share of a loan not redeposited into the banking system.
Redeposit fraction
The fraction of one round's deposit that becomes the next round's deposit.
Money multiplier
The long-run geometric ratio of total deposits to the initial deposit under the model assumptions.