Lesson summary: banking and the expansion of the money supply (article) | Khan Academy (2024)

In this lesson summary review and remind yourself of the key terms and calculations related to fractional reserve banking, required reserves, excess reserves, and the money multiplier.

Lesson Summary

Money is created when the government prints it, right? That’s only partially true because banks create money too. Banks don’t literally print their own currency (save for a few banks in Scotland, who do just that). So how does a bank “create” money?

Recall that the narrowest definition of the money supply is M1, which includes money in circulation (not held in a bank) and demand deposits held inside banks. In the United States, less than half of M1 is in the form of currency—much of the rest of M1 is in the form of bank accounts.

Every time a dollar is deposited into a bank account, a bank’s total reserves increases. The bank will keep some of it on hand as required reserves, but it will loan the excess reserves out. When that loan is made, it increases the money supply.

This is how banks “create” money and increase the money supply. When a bank makes loans out of excess reserves, the money supply increases. We can predict the maximum change in the money supply with the money multiplier.

Key Terms

Key termDefinition
Bank(sometimes called a commercial bank) A financial institution that accepts deposits and makes loans; banks are sometimes referred to as “depository institutions.”
Central bank(sometimes called a reserve bank or banking authority) an institution that manages a country’s money supply and monetary policy
Financial intermediarya middle-person in a financial transaction; a bank is an intermediary that coordinates borrowing and lending by combining the deposits of many agents into loans.
Assetssomething of value to the agent that holds it; a bank’s assets include real assets owned by the bank (such as a building), the money they hold, and financial assets such as bonds and loans.
Liabilitiesobligations to pay back; to a bank, your savings account is a liability because you might show up one day and want the money you deposited back.
Fractional reservesthe practice of keeping a percentage of deposits on hand but loaning out the rest
Reserve requirementa legal obligation to keep a minimum amount of reserves; if the reserve requirement is 20% and you deposit $100 in a bank, the bank must keep $20 of that in its vaults, but it can loan out the rest.
Excess reservesthe remainder of the deposited money that banks are not required to keep on hand; banks can make loans out of excess reserves or choose to keep excess reserves in their vaults.
Fully loaned outa situation in which a bank has only required reserves and keeps no excess reserves; when a bank is fully loaned out it cannot make any additional loans.
T-accounta tool for describing the financial position of a business by showing assets (on the left) and liabilities (on the right) in a table; each side of the table must equal the other side.
Money multiplierthe ratio of the money supply to the monetary base (money in bank vaults and money in circulation); the money multiplier tells us how many additional dollars will be created with each addition to the monetary base, such as when there is a $1 increase in a bank’s reserves.

Key Takeaways

Assets and Liabilities

Banks, like any other business, need to keep track of their assets and liabilities. T-accounts are tables that banks use to keep track of assets and liabilities.

Let’s create a T-account for a bank that has just opened for business, First Bank of Pulitzer. Nobody has deposited any money yet, so other than its obligations to the bank owners and the real assets that the bank has (like the bank building itself), the bank’s T-account is empty:


Now suppose you win $100 in a poetry writing competition. Congratulations! You deposit your winnings in a First Bank of Pulitzer checking account. That deposit creates two entries on the bank’s balance sheet. The $100 in cash creates an entry on the asset side because the money is an asset for the bank (because they can put that money to use by loaning it out). But, the bank must give you back that money as well. That obligation is a liability, so there is a $100 entry on the liabilities side as well.

The bank’s balance sheet now looks like this:

Cash $100$100 Your Deposit

Fractional reserve banking

Banks are more than just a vault to keep money in. If banks just acted as a storage facility for money, that wouldn’t be a very profitable business. The $100 you deposited from your groundbreaking verses will be used to make loans. Banks profit from making loans by charging interest.

But the new First Bank of Pulitzer has a problem. They want to make loans (because that is how they earn a profit). But at some point, they also need to pay back the money that people have deposited into the bank. This is where reserves come in.

Reserves are the amount of money that banks keep in vaults, and they are a fraction of all deposits made. In most countries, banks are heavily regulated and are required to keep a minimum percentage of all deposits, just in case someone wants to withdraw some money. This minimum percent is the reserve requirement.

For example, suppose the reserve requirement is 20%. The bank would need to keep $20 of your $100 on hand. We can break this down in our T-account:

Required reserves $20$100 Your Deposit
The rest of the cash $80

Excess reserves allow expansion of the money supply

To understand how banks create money, let’s take a step back. What if that poetry competition money was the only money that existed in the economy. Before you deposit the money in the bank, let’s calculate the money supply:

M1=currency in circulation+deposits=$100+$0

Once you deposit your money in the bank, M1 doesn’t change; only the composition of the money supply changes:


How does the First Bank of Pulitzer bank create more money out of this $100? Our bank now has $80 just sitting around. This is the bank’s excess reserves - the extra money beyond what they must keep in required reserves. The bank can do one of two things with that money:

  • Keep it in the bank (just in case you want to withdraw more than $20)
  • Loan it out

In the real world, your deposit wouldn’t be the only deposit in the bank. Usually, only a small number of people want to withdraw their money on a given day. So, the bank might want to loan out that money to earn a profit.

Now, suppose Sylvia shows up at the bank and wants to borrow $50. Let’s see how the bank’s loan to Sylvia impacts their T-account and the money supply:

Required reserves $20$100 Your Deposit
Loan to Sylvia $50
Excess reserves $30

M1 has changed as well. Remember, your $100 deposit is still your money. If you check your account balance, it still says you have $100. But Sylvia now has $50 in cash in her pocket, too:

M1=cash in circulation+deposits=$50+$100=$150

The money multiplier determines the size of the expansion

Banks can’t create an unlimited amount of money. The money multiplier determines the limit of how much money a bank can create. The money multiplier is how much the money supply will change if there is a change in the monetary base.

There are several reasons that the actual increase in the money supply will be smaller than the simple money multiplier predicts, including:People decide not to deposit money into banks, so money “leaks” out of the banking systemBanks decide not to loan out everything and keep some excess reserves

Sure! Let’s take another look at the bank. Right now, they still have $30 sitting around. Suppose they lend that out to Ted. Now, the bank’s T-account looks like this:

Required reserves $20$100 Your Deposit
Loan to Sylvia $50
Loan to Ted $30

What impact does that have on the money supply? Well, now Ted also has some money in his pocket:

M1=cash in circulation+deposits=($50+$30)+$100=$180

Sylvia and Ted take the money they borrowed and decide to take a trip to Seamus’s House of Donuts and spend their combined $80 on chocolate donuts. Seamus takes that money and deposits it into the bank. Now the bank has $80 in its vaults (an asset) and a new liability (the money the bank owes Seamus). We can note these changes in the bank’s T-account:

Required reserves $20$100 Your Deposit
Loan to Sylvia $50$80 Seamus's deposit
Loan to Ted $30
Cash $80

We can also track the changes in the money supply:

M1=cash in circulation+deposits=$0+$180=$180

Notice that the money supply hasn’t changed. But, the bank must keep 20% of that $80 on hand. So it stores $16 (20% of $80) and has $64 in excess reserves. Gwendolyn borrows that money to spend on writing journals. When the loan is issued, the money supply increases again:

M1=cash in circulation+deposits=$64+$180=$244

Each time money is deposited, the reserve requirement (rr) is kept, but the rest can be loaned out.


As we have seen before with other multipliers (like the expenditure multiplier and tax multiplier), this kind of expansion can be simplified to

Total increase in money supply=$100×1rr

So, if the bank never keeps any excess reserves on hand, and all money is always deposited into banks, your $100 prize will turn into a money supply of $500:


Key equations

The money multiplier

The money multiplier determines the maximum expansion of the money supply that will occur when new money is introduced into the banking system. If you know the size of the reserve requirement, you can use this to figure out the largest change in the money supply that is possible if the central bank creates new money. The money multiplier (MM) is calculated as follows:

MM=1rr,whereMM=money multiplierrr=reserve requirement

For example, if the reserve requirement is 25%, the money multiplier is 4:


So, if I know that the money multiplier is 4, then if the central bank creates $100 in money, the money supply will increase by $400 at most.

In reality, however, the money multiplier is more complicated than this, which is why it is sometimes called the simple money multiplier. The simple money multiplier assumes that:

  • Banks never keep any excess reserves, and
  • People keep all money in banks (in other words, if you get $20, you immediately deposit it).

Now suppose instead that you know the actual change in the money supply from a change in the monetary base. With this information, you can find the actual money multiplier, rather than the theoretical maximum change. To find the actual money multiplier, you divide the money supply by the monetary base:



AMM=actual money multiplierMS=money supplyMB=monetary base

For example, if M1 is $100 million, and there is $40 million in circulation and $10 million in reserves at banks, then the actual money multiplier is:


In this case, the more realistic money multiplier is only 2, rather than the simple money multiplier that is predicted using the reserve requirement.

The maximum predicted change in the money supply from an increase in the monetary base

Total change inMS=change inMB×MM

For example, suppose the First Bank of Pulitzer bank buys a bond from Langston for $200. They deposit $200 into his bank account. The reserve requirement is 25%. If there are no leakages from the banking system (banks fully loan out, and everyone keeps all of their money in the bank), the maximum total change in the money supply from the central bank buying a bond is

Maximum total change inMS=change inMB×MM=$200×4=$800

Calculating excess reserves

Excess reserves=Deposits(Deposits×reserve requirement)

For example, if Maya deposits $4000 into the bank, and the reserve requirement is 10%, the bank must keep $400 in reserves but has excess reserves of

Excess reserves=$4000($4000×10%)=$4000$400=$3600

Maximum new loans possible from a deposit

Maximum increase in loans=(Depositreserves)×Money multiplier

For example, if the money multiplier is 4, banks fully loan out, and all money is deposited into banks, then the total amount of new loans that can be made from Maya’s deposit is


Common Misperceptions

  • Some learners get confused about what the simple money multiplier represents. The simple multiplier 1rr is the maximum change in the money supply. In all probability, the final increase in the money supply will be far smaller due to leakages from the financial system.
  • Printing money and creating money is not the same thing. Printing money creates currency, but the amount of money that exists at any point in time (in other words, the money supply) is cash and deposits. The pivotal moment in the creation of money is lending: when loans are made, money is created.
  • It might seem strange that a bank account is a liability. To you, the owner of the account, the account is an asset. But to the bank, who has to return that money to you on demand, it is a liability.
  • As a new learner, it might be confusing about which stage in this process creates money. It is the loan. If a bank does not loan out from a deposit, no new money is created.

Discussion questions

Question 1

There is currently $100,000 in circulation outside of banks in the nation of Rhyme. The following is a simplified balance sheet for the Bank of Rhyme. However, some of the data on the balance sheet is missing.

Required reserves $20,000Demand deposits $200,000
Excess reserves $50,000
Loans $ _

Assume that this bank has no assets other than cash and loans.

  1. What is the value of the loans that this bank has made? Explain how you know this.

  2. What is the reserve requirement?

  3. If Ted withdraws $10,000 from his checking account at the Bank of Rhyme:

    a. What is the initial effect of the withdrawal on M1?

    b. What effect will this have on the bank’s total reserves, required reserves, and excess reserves?

  1. The bank has $130,000 in loans outstanding. The asset and liabilities sides must equal each other on the balance sheet. Required reserves and excess reserves are worth $70,000 total, so:


  1. The reserve requirement is 10%. From the equation to calculate the amount of reserves required:

Deposits×reserve requirement=required reserves$200,000×rr=$20,000rr=$20,000$200,000rr=10%

3a. M1 will not change. Before the withdrawal:

M1=cash in circulation+demand depositsM1=$100,000+$200,000

After the withdrawal:


Only the composition of the money supply changes, not the quantity of money. No money is created or destroyed when money is withdrawn from or deposited in a bank

3b. Before the withdrawal, the bank has $70,000 in total reserves:


When he withdraws $10,000, total reserves decrease by $10,000 to $60,000. The bank only needs $19,000 in reserves, so excess reserves are:


Question 2

The balance sheet for The First Bank of Pulitzer is shown below. Assume the reserve requirement is 5%.

Total reserves $35,000Demand deposits $500,000
Home loans $445,000
Government bonds $20,000

a. What is the total amount of new loans that this bank can make? Explain.

b. Now, suppose that the First Bank of Pulitzer, and all other banks in the financial system, loan out all excess reserves. Calculate the maximum total change in deposits throughout the banking system. Show all work.

c. Assume that there are no leakages from the financial system. What will be the change in total reserves throughout the banking system? Explain.

d. Suppose the central bank in this country buys $5,000 of the government bonds from The First Bank of Pulitzer. Will the money supply increase, decrease, or stay the same? Explain.

a. This bank can make $10,000 in additional loans. The required reserves for $500,000 are:


They have $35,000 in total reserves, so excess reserves are:


b. To find the total change in demand deposits:

Total change in demand deposits=excess reserves×money multiplier=$10,000×1rr=$10,000×10.5=$10,000×20=$200,000

c. The total change in reserves will be $0. The monetary base is money in circulation plus money in banks. The monetary base does not change when loans are made. If all money is redeposited into banks, and all excess reserves are fully loaned out, all of the monetary base will be in the form of currency in bank vaults.

d. The money supply will increase. When the central bank buys the bonds, it pays $5,000 in exchange for the bonds. The bank now has $5,000 in excess reserves that can be loaned out. By loaning that out, money will be created.

Lesson summary: banking and the expansion of the money supply (article) | Khan Academy (2024)
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