Money Multiplier: Definition & Formula

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  • 0:02 Money Multiplier Definition
  • 2:19 Money Multiplier Formula
  • 4:19 Lesson Summary
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Lesson Transcript
Shawn Grimsley

Shawn has a masters of public administration, JD, and a BA in political science.

Expert Contributor
Steven Scalia

Steven completed a Graduate Degree is Chartered Accountancy at Concordia University. He has performed as Teacher's Assistant and Assistant Lecturer in University.

Banks actually create money by lending money. In this lesson, you'll learn about the money multiplier, including what it is, its formula, and how to use it. You'll also have a chance to take a short quiz after the lesson.

Definition of Money Multiplier

The money multiplier is the amount of money that banks generate with each dollar of reserves. Reserves is the amount of deposits that the Federal Reserve requires banks to hold and not lend. Banking reserves is the ratio of reserves to the total amount of deposits.

The money multiplier is the ratio of deposits to reserves in the banking system. Why is this important? Let's take a look at an example to illustrate the power of banks to literally create money out of thin air.

Imagine that you are president of a large bank. The Fed requires that you hold 10% of your deposits in reserves, a reserve ratio of 1/10. This means that for every $1.00 of deposits, you can only lend out $0.90. The total value of your bank's deposits is $100,000,000. You want to maximize your bank's profits, so you loan out all of the $90,000,000. All of sudden, you've just increased the supply of money from $100,000,000 to $190,000,000!

Here's how you did it. Your depositors still have $100,000,000 with you, but only on paper. They can come in any time and get their money. However, since not everyone wants, or needs, their money at the same time, your reserves of $10,000,000 will cover the normal demand for withdrawals.

At the same time, you have distributed $90,000,000 in loan funds to your borrowers - that's real money going out the bank's door. Your borrowers will spend that money on houses, cars, factories, and machinery, among countless other purchases. The sellers who receive the loaned money in exchange for their goods or services will deposit their revenue in banks. And of course, the banks will turn around and loan out another 90% of that $90,000,000, and the cycle will start over again.

So, what does this have to do with the money multiplier? The money multiplier will tell you how fast the money supply from the bank lending will grow. The higher the reserve ratio is, the less deposits will be available for lending, resulting in a smaller money multiplier. Now, let's see how to calculate the money multiplier.

Money Multiplier Formula

The money multiplier is the reciprocal of the reserve ratio:

Money multiplier = 1 / R, where R is the reserve ratio

Imagine you are still the president of that bank, and you get notice from the Fed that it is loosening its minimum reserve requirements from 10% to 5%. What is the new money multiplier?

Money multiplier = 1 / R, where R is the reserve ratio

You can get the ratio by converting the percentage into a fraction by simply dividing it by 100 and then simplifying the fraction:

5 / 100 = 1/20

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Additional Activities

Money Multiplier - A Practical Exercise:

The following exercise is designed to help students apply their knowledge of the Money Multiplier concept and its relationship with the Required Reserve Ratio.


You are an Economist studying the monetary policy of Boomer Country, a remote tropical island that is known to have a lot of wealthy baby-boomers enjoying their retirement. The Central Bank of Boomer Country maintained its required reserve ratio steady at 25% at its last meeting. Boomer Country has a handful of banks, and they all wish to maintain only the minimum amount of reserves necessary (i.e., there are typically no excess reserves).

1. Calculate the current money multiplier for Boomer Country. Explain what exactly does that mean?

2. Boomer Country's most popular bank has $300 Million in bank deposits. How much money is being generated from the bank's excess reserves?

3. Assume now that the Central Bank wishes to lower the required reserve ratio to 16%. Calculate the new money multiplier.

4. Will the new required reserve ratio discussed in #3 increase or decrease the amount of money in the economy? Why?



Money Multiplier = 1 / Reserve Ratio

Reserve Ratio = 25/100 = 1/4

Money Multiplier = 1 / (1/4) = 4

The money multiplier is thus 4.


Let's first compute the excess reserves (i.e. the funds that can be loaned out).

Excess Reserves =Bank Deposits - (Bank Deposits * Reserve Ratio)

= $300 Million - ($300 Million * 25%)

=$225 Million

Increase in Money Supply = Additional money loaned out * Money Multiplier

= $225 Million * 4

= $900 Million

The answer is $900 Million.


Money Multiplier = 1 / Reserve Ratio

Reserve Ratio = 16/100 = 4/25

Money Multiplier = 1 / (9/50) = 6.25

The money multiplier is thus 6.25.


This will increase the amount of money in the country because a higher money multiplier leads to more cash being generated for every single dollar of reserves.

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