Money Multiplier Calculator

Calculator Inputs

Enter banking assumptions, then calculate multiplier behavior, deposit recycling, and money supply effects under both simple and adjusted frameworks.

Example Data Table

This sample shows how the calculator behaves with common textbook-style assumptions for reserve requirements, excess reserves, and cash leakage.

Item	Sample Value
Monetary Base	100,000.00
Initial Deposit	50,000.00
Required Reserve Ratio	10.00%
Excess Reserve Ratio	2.00%
Currency Ratio	15.00%
Simple Multiplier	10.0000
Adjusted Multiplier	4.2593
Adjusted Money Supply	425,925.93
Maximum Deposit Stock	370,370.37

Formula Used

The calculator combines the textbook reserve-only model with an adjusted model that includes excess reserves and cash withdrawals.

Simple money multiplier: m = 1 / rr

Adjusted money multiplier: m = (1 + c) / (rr + er + c)

Deposit multiplier: d = 1 / (rr + er + c)

Money supply from base: M = Monetary Base × Adjusted Multiplier

Round recycling factor: q = 1 − rr − er − c

Finite deposit expansion: Total Deposits = Initial Deposit × (1 − qⁿ) / (rr + er + c)

Variable Meanings

rr is the required reserve ratio, er is the excess reserve ratio, c is the currency ratio, and n is the number of lending rounds.

How to Use This Calculator

Enter the monetary base to estimate the broad money supportable under your assumptions.

Set the required reserve ratio based on policy or your scenario.

Add any excess reserve ratio to reflect cautious bank behavior.

Enter the currency ratio to model cash withdrawn by households and firms.

Use an initial deposit and simulation rounds to inspect deposit creation step by step.

Optionally add a policy base change to estimate how an injection or withdrawal shifts money supply.

Click calculate to see summary cards, the graph, and the deposit expansion table.

Export the output with the CSV or PDF buttons for reporting.

FAQs

1. What does the money multiplier measure?

It estimates how much money supply or deposits can be supported by a given monetary base. Higher leakages and reserve holdings usually lower the multiplier.

2. Why is the adjusted multiplier smaller than the simple multiplier?

The adjusted version subtracts extra frictions. Currency withdrawals and excess reserves prevent all loaned funds from returning as deposits, so money creation weakens.

3. What is the currency ratio in this calculator?

It is the portion of deposits the public prefers to hold as cash. More cash outside banks reduces redepositing and slows deposit expansion.

4. How does a higher reserve ratio affect results?

A higher required reserve ratio raises the drain on each deposit round. That reduces lending capacity, deposit growth, and the multiplier.

5. Why include both monetary base and initial deposit?

The monetary base estimates system-wide supportable money. The initial deposit powers the round-by-round simulation, showing how one deposit propagates through lending cycles.

6. Does this calculator predict actual future money supply perfectly?

No. Real outcomes depend on regulation, loan demand, interest rates, capital constraints, and central bank operations. This tool is a structured scenario model.

7. What does the policy base change field do?

It estimates the money supply effect of an increase or decrease in the monetary base. The calculator shows both simple and adjusted impacts.

8. When is the simple model still useful?

The simple model is useful for quick teaching examples and rough intuition. It highlights reserve requirements clearly, even though it ignores practical leakages.