Money multiplier calculator

Enter a deposit and the reserve requirement. You get the money multiplier, the most the money supply can grow, and bars that show each bank keeping a share as reserves and lending the rest, round after round, until the chain fades out.

Inputs

In any one unit: dollars, or millions of dollars as in the OpenStax example.

Cash that is deposited was money before, so only the loans it makes possible are new. New reserves are new money, so the first deposit counts too.

The share of every deposit banks must keep as reserves. The multiplier is 1 divided by it.

Optional. Banks that hold more than they must lend out less, which shrinks the multiplier.

Optional. Money kept in a wallet or a mattress never reaches a bank, so the chain loses a share each round.

How many rounds of lending the bars show. The result counts every round.

Largest possible increase in the money supply

90

A deposit of 10 with a reserve requirement of 10% can grow into total deposits of 100 (10 × 10), so the money supply rises by 90: the 10 was already money.

Money multiplier
10
Total deposits
100
Reserves banks keep
10
Loans made
90
Done after 6 rounds
46.86 of 100 (47%)
How one deposit grows through rounds of lending
101928.137.2946.5655.96Round of lendingAll deposits created: 100123456all later rounds 53.1Where it ends up: reserves + loansLoans 90
  • Kept as reserves
  • Lent out, then deposited again
  • Later rounds, not drawn

A deposit of 10 with a reserve requirement of 10%. Round 1: the bank keeps 1 and lends 9, which comes back as a deposit of 9 in round 2. All the rounds together create deposits of 100, of which banks keep 10 in reserves and lend 90. The money supply rises by at most 90.

How to read this graph

  • Each column is one round of lending. Round 1 is the deposit you started with. The bank keeps part of it as reserves (dark) and lends the rest (light).
  • The loan becomes the next column. The borrower spends it, and whoever receives it deposits it in a bank, so round 2’s deposit is round 1’s loan.
  • Each column is shorter than the last by the share the bank kept back. The shorter the columns shrink, the more rounds the chain needs, and the larger the total.
  • The long bar underneath cuts all the deposits that end up in the banking system into those rounds. The pale block at the end is every later round, added together, which the columns have no room to show.
  • The bottom bar is the banks’ combined balance sheet: reserves plus loans equal deposits, which is what the Wisconsin handout asks you to fill in at the end.

How it works

nothing leaking, reserve requirement r (0.10 for 10%), first deposit D:
each round: a bank takes in a deposit d, keeps r × d as reserves and lends (1 − r) × d
the loan is deposited again: next deposit = (1 − r) × d
money multiplier = 1 ÷ r
total deposits = D × (1 ÷ r) = D ÷ r
reserves = D       loans = D × (1 ÷ r − 1)       (D = the first deposit)
money supply rises by:   cash deposited:  loans = D × (1 ÷ r − 1)
new reserves:    total deposits = D ÷ r
with extra reserves e and a share c of each loan kept as cash:
next deposit = (1 − r − e) × (1 − c) × d
total deposits = D ÷ (1 − (1 − r − e)(1 − c))
  • The multiplier only depends on the reserve requirement. The size of the deposit just scales the answer.
  • The rounds form a geometric series, each one a fixed share of the one before. Adding them gives the closed form, so the calculator does not need to run a loop; the columns are only there to show you the pattern.
  • Reserves equal the money you started with. The banks together never hold more reserves than the original cash or new reserves. They turn the rest of the deposits into loans.
  • A reserve requirement of 0% has no limit: every loan comes back in full, so the series never ends. The calculator says so instead of giving a number.
  • Amounts carry no unit. Use dollars, or millions of dollars as OpenStax does.

Worked example

OpenStax’s Singleton Bank has $10 million of deposits and must keep 10% as reserves. Open it in the calculator (amounts in millions).

  • Round 1: the bank keeps $1 million and lends $9 million to Hank’s Auto Supply, who deposits it at First National.
  • Round 2: First National has a deposit of $9 million, keeps $0.9 million and lends $8.1 million to Jack’s Chevy Dealership. After the first loan the money supply is $10 million + $9 million = $19 million, as OpenStax says.
  • The multiplier: 1 ÷ 0.10 = 10.
  • All the rounds together: deposits of 10 ÷ 0.10 = $100 million. Banks keep $10 million in reserves and lend $90 million. The money supply rises by 10 × $9 million = $90 million.

More to try:

Tips

  • Ask where the money comes from. Cash deposited is already money, so only the loans are new. New reserves are new money, and the first deposit counts. Books differ in which they mean by “the money supply increases by”, so match your course.
  • Type the requirement as a percent. 10% is 10, not 0.1.
  • Counting rounds: the first few rounds do most of the work at a low reserve requirement, but at 10% it takes about 22 rounds to reach 90% of the limit. Use more rounds to watch it converge.
  • This is the textbook model. It leaves out banks that lend less than they could, borrowers who repay, and everything the central bank does besides setting reserves. Use it to understand the mechanism and to check homework, not to predict the real money supply.
  • Reserves and cash together never exceed the original amount: if your answer for reserves is bigger than the deposit, something is wrong.

FAQ

What is the money multiplier, and what is its formula?

It is the number of times an initial amount of reserves can be multiplied into deposits as banks lend and the loans are deposited again. With a reserve requirement of 10% it is 1 ÷ 0.10 = 10. OpenStax multiplies it by the excess reserves of the first bank to get the change in the M1 money supply, which for Singleton Bank is 10 × $9 million = $90 million.

Why does the headline say $90 million when the deposit was $10 million and the total comes to $100 million?

Because the $10 million was already money before it was deposited. Total deposits grow to $100 million, but only $90 million of that is new. The calculator’s “cash already in circulation” choice reproduces that count: for cash deposited, the rise in the money supply equals the loans made. If the money is new, as when a central bank buys bonds and the seller deposits the payment, the first deposit counts as well. UW–Madison’s example gives $1 million of bond purchases a $10 million rise at a 10% requirement.

Why is the answer called the largest possible increase?

It assumes banks lend every dollar above the required reserves and that every loan comes back into a bank as a deposit. OpenStax warns that banks can choose to hold extra reserves, especially in a recession, and that people who keep cash at home, which it calls mattress savings, keep banks from lending it on. Either one makes the real multiplier smaller.

What happens if banks hold extra reserves or people keep some cash?

Each round is smaller, so the total is. The optional inputs add both: extra reserves raise the share each bank keeps, and cash kept takes a share of each loan out of the chain. With a 10% requirement, 5% extra reserves and 20% of each loan kept as cash, each deposit is (1 − 0.15) × (1 − 0.2) = 0.68 times the last, so deposits end at 10 ÷ 0.32 = 31.25 instead of 100. That formula is the sum of the rounds worked out here rather than one quoted from a book, so check it against your course’s version.

What happens when the central bank changes the reserve requirement?

A higher requirement means a smaller multiplier, and a lower one a bigger multiplier. OpenStax notes that the Federal Reserve can raise or lower the requirement as a policy move to affect the quantity of money. The UW–Madison handout shows the effect: the same $1 million bond purchase adds $10 million at 10% and $5 million at 20%, and selling $1 million of bonds at 20% takes $5 million out.

Sources

  1. 14.4 How Banks Create Money, OpenStax, Principles of Macroeconomics 3e (Rice University). Singleton Bank with $10 million of deposits and a 10% reserve requirement lends $9 million; First National lends $8.1 million; the multiplier is 1 ÷ the reserve requirement = 10, and 10 × $9 million of excess reserves is a $90 million change in M1. Also the cautions about extra reserves and cash kept out of banks.
  2. Econ 102 Discussion Section Handout #11: T-Accounts and the Money Multiplier (answers), University of Wisconsin–Madison, Economics 102 (course site of Prof. Emily Kelly, Fall 2007). Susan deposits $3,000 with $1 of reserves for every $10 of deposits. Bank #1 lends $2,700, Bank #2 lends $2,430, and all banks together end with $3,000 of reserves, $27,000 of loans and $30,000 of deposits, a multiplier of 10. Also open market operations (a $1 million bond purchase gives $10 million at 10% and $5 million at 20%).

Formula and sources last checked September 30, 2026. How we test formulas.