Formula of Money Multiplier (Table of Contents)
What is the Money Multiplier Formula?
Money Multiplier can be defined as the kind of effect which can be referred to as the disproportionate rise in the amount of money in a banking system that results from an injection of each dollar of the reserve. The formula for Money Multiplier is represented as follows,
 It is the amount of money that the economy or the banking system will be able to generate with each of the reserves of the dollar. Definitely, this will depend on the reserve ratio.
 The more the amount of money the bank has to hold them in reserve, the less they would be able to lend the loans. Thus, the multiplier holds an inverse relationship with the reserve ratio.
Examples of Money Multiplier Formula
Let’s see some simple to advanced examples of the Money Multiplier equation to understand it better.
Example #1
If the reserve ratio is 5.5% prevailing as per current conditions, then calculate the money multiplier.
Solution:
Given,
 Reserve Ratio = 5.5%
Therefore, the calculation of money multiplier will be as follows,
Money Multiplier will be –
=1 / 0.055
= 18.18
Hence, the money multiplier would be 18.18
Example #2
Country WWF was one of the most successful countries in the world in terms of handling the country’s financial and economic conditions which were due to Mr. Right who was leading the central bank. Mr. Right retired a few years ago and then he was succeeded by Mr. Medium who is looking after the current affairs of the central bank. It was observed that the country is facing high inflation compared to a few years ago and the central bank now is interested in reducing the inflation and one way which they have thought of it by injecting liquidity in the market.
Due to the peak of currency depreciation, the central bank is hesitant to print new currency and is also not interested in lowering the Bank rates as that might result in the outflow of FII funds. In the meeting held, where the ExGovernor of central bank Mr. Right was also invited, where he suggested that reserve ratio can be reduced from existing 6% to 5%. The current money supply in the market is US$35 trillion and Mr. Right also suggested to inject US$1 trillion for which they are already held in reserves. The Banks’ target money supply in the market after this action is US$54 trillion.
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You are required to calculate the money multiplier and whether the action was taken by a central bank with suggestions from Mr. Right be impactful? What will happen if the reserve ratio is not changed?
Solution
Given,
 Reserve Ratio = 5.5%
Therefore, the calculation of money multiplier will be as follows,
Money Multiplier will be –
= 1 / 0.05
=20 times
Hence, this would mean that if 1 unit of money is deposited in the economy, it shall multiply that money in the economy as 20 units of money.
Therefore, if the central bank is targeting to inject US$1 trillion into the market, then that would lead to money supply of US$1 trillion x 20 times which equals to US$20 trillion and already there is a money supply of US$35 trillion and with this US$20 trillion it would reach to US$55 trillion economies in virtual terms. The action plan was US$54 trillion and per this ratio, there is a surplus of US$1 trillion.
And had the central bank kept reserve ratio 6% then the money multiplier will be 1/0.06 which is 16.67 and that if kept then the target of the central bank will not be reached.
Example #3
Two students were arguing with each other on the topic of a money multiplier. The first student says if the reserve ratio is kept low, the more money supplies the lower the inflation in the economy whereas the second student stated that the higher the ratio, the less the money supply and that would actually reduce the inflation. You are required to validate which statement is correct taking as an example of 7% versus 8% as the reserve ratio.
Solution:
We are given an example of the reserve ratio and from this, we can calculate money multiplier from below formula:
Case I
 Reserve Ratio – 7%
Therefore, the calculation of money multiplier will be as follows,
Money Multiplier will be –
= 1 / 0.07
= 14.29
Case II
 Reserve Ratio = 8%
Therefore, the calculation of money multiplier will be as follows,
Money Multiplier will be –
= 1 / 0.08
= 12.50
From above, it can be inferred that keeping a reserve ratio at 7% will infuse more money as it will be more circulated whereas keeping at 8%, will infuse less money.
Hence, if more money comes in the market, then inflation will increase and vice versa will be the case, therefore the statement made by student 2 is correct that higher reserve ratio will reduce inflation and the statement made by student 1 is incorrect.
Money Multiplier Formula Calculator
You can use this money multiplier formula calculator
Reserve Ratio  
Money Multiplier  
Money Multiplier = 


Relevance and Uses
As with almost all of the countries that are for the banking system, commercial banks are only required to hold for all deposits as a certain percentage as reserves which is termed as the reserve ratio. The remaining deposits than can be utilized to lend out the loans and this would then increase the supply of money. However, it must be noted that the creation of money will not pause here. The newly created money will be further deposit in a different bank, which in turn shall lend a loan for a fraction of that money to several different customers and this will keep ongoing. This process can be repeated forever in theory.
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