How much must the bank keep on hand if the required reserve is 10% and there is a deposit of $100?

The deposit multiplier is the multiple by which banks can lend out deposited money based on the existing reserve requirement. It plays a key role in the fractional reserve banking system, and is used to help stabilize the money supply.

Here’s a closer look at how the deposit multiplier works, how it’s calculated, and why it’s important.

Definition and Examples of a Deposit Multiplier

The deposit multiplier represents the maximum amount of money a bank can lend out for every dollar it holds in reserves.  The deposit multiplier is usually expressed as a percentage of the total amount of money held in demand deposit accounts, such as checking and money market accounts.

• Alternate names: Deposit expansion multiplier, simple deposit multiplier

For example, if a bank has $100 million in demand deposits and a reserve requirement of 5%, it must keep $5 million in its reserve, but can lend the other $95 million (or 95%) out in the form of loans and credit. This is called fractional banking, and it’s a tool used to help expand the economy, in part, by offering consumers money they can borrow to make purchases.

How a Deposit Multiplier Works

Whenever you deposit money into your bank account, your bank is legally required to hold onto a percentage of it. This percentage is known as the “reserve requirement,” and it’s set by the Federal Reserve.

For example, suppose the federal reserve requirement is 5% and you deposit $1,000 into your bank account. Your bank puts $50 in its reserves and loans the other $950 out to someone else. That person can then spend the full $950 they borrowed, and when the bank’s payees deposit that money into each of their bank accounts, their banks repeat the process of saving some and lending out the rest. Thus, the bank multiplies your initial $1,000 deposit into even more money.

Note

In theory, deposit multipliers work by allowing the Federal Reserve to control the deposit creation process. Since banks are required to keep a certain percentage of their deposits on hand, the Federal Reserve can change the reserve requirement percent to control how many new deposits are created.

The deposit multiplier formula looks like this:

Deposit multiplier = 1 / reserve ratio 

So if the required reserve ratio is 20%, the deposit multiplier is five. This means that for every $1 the bank has in reserves, it can increase the money supply by up to $5. If the reserve ratio was 10%, the deposit multiplier would be 10, and the bank could increase the money supply by $10 for every $1 in reserves.

In essence, the lower a bank’s required reserve ratio, the higher the deposit multiplier will be and the more money it can lend out to customers.

The Deposit Multiplier and the Economy

The deposit multiplier is one of the major mechanisms central banks and financial authorities such as the Federal Reserve use to control the money supply in an economy.

Note

While deposit multipliers aren’t used by all central banks, they’re very important in maintaining a country's monetary policy.

The Fed uses three other monetary policy tools to control the money supply in an economy. The first is open market operations, which involve purchasing or selling government securities to affect the money supply. The second is reserve requirements, which are mandatory deposit amounts financial institutions have to keep on deposit at a bank. The third is interest rates, which influences the interest rates offered by banks and lenders.

Deposit Multiplier vs. Money Multiplier

The deposit multiplier sometimes gets confused with “money multiplier,” but the two are different concepts.

Think of the deposit multiplier as a best-case what-if scenario. It represents the maximum amount of money banks could potentially create through lending. In reality, this maximum amount is never reached because banks don’t lend out 100% of their excess reserves, and customers don’t always spend 100% of their loans. 

Thus, the money multiplier represents the actual change to the money supply created through lending. It’s usually lower than the deposit multiplier because it accounts for “leaks” that occur when borrowers hold onto some of their loans in cash or exchange them for other currencies.

Key Takeaways

• The deposit multiplier describes how changes in banks' reserve requirements affect the amount of money or credit they can lend out through deposit expansion.
• The deposit multiplier is the reciprocal of the required reserve ratio. If a bank is required to keep 20% on hand, the deposit multiplier is five.
• The deposit multiplier represents the maximum amount of money a country could potentially create through bank lending. Think of it as a best-case scenario.
• The money multiplier, on the other hand, represents the actual change to the money supply created through lending. It’s usually lower than the deposit multiplier because banks don’t lend all their reserves, and borrowers don’t spend all their money.

What is the money multiplier if the reserve requirement is 10 %?

What would happen if the reserve requirement was 100%?

Why is the bank required to keep only 10% from the money deposit as reserve?

How much must banks keep on reserves?