Skip to content

CFA Level I Exam · Monetary Policy

Money Creation and the Money Multiplier Formula

Updated 7 October 2026 · Fact-checked

Money serves as a medium of exchange, a unit of account and a store of value. Under fractional reserve banking, banks lend out deposits beyond required reserves, creating new deposits. In the simple model, the money multiplier is 1 ÷ reserve requirement. Quantity theory says M × V = P × Y.

Understand Money: Functions, Creation and Money Multiplier

Money is anything generally accepted as payment for goods and services and for settling debts. It does three jobs. It is a medium of exchange, so you avoid barter and the need for a double coincidence of wants. It is a unit of account, so prices are quoted in one common measure. It is a store of value, so you can hold purchasing power and spend it later. Inflation erodes this third function.

The quantity of money is measured at two broad levels. Narrow money is the most liquid form: notes and coins in circulation plus balances in checking (demand) deposits. Broad money includes narrow money plus less liquid items such as savings and time deposits and some money market funds. Exact definitions differ by country, so learn the idea: broad money is narrow money plus assets that are close substitutes but harder to spend.

In fractional reserve banking, banks keep only a fraction of deposits as reserves and lend out the rest. A loan is spent, the payee deposits it in another bank, and that bank lends out its excess reserves too. Each round creates new deposits. Total deposits rise by a multiple of the original injection of reserves.

The simple money multiplier is 1 ÷ reserve requirement. With a 10% reserve requirement, the multiplier is 10. In reality the multiplier is smaller, because banks may hold excess reserves and the public holds some cash instead of depositing it. Money creation is also limited by loan demand, not just reserves.

The quantity theory of money uses the equation of exchange: M × V = P × Y. M is the money supply, V is velocity (how often money changes hands), P is the price level and Y is real output. If V and Y are stable, a rise in money growth leads to a proportional rise in the price level. Monetarists use this to argue that inflation is ultimately a monetary phenomenon.

Key formulas to remember

Money multiplier (simple)
Money multiplier = 1 ÷ reserve requirement
Assumes banks hold no excess reserves and the public holds no cash. Use the decimal form of the ratio.
Change in money supply
Δ Money supply = new reserves × money multiplier
Use the new excess reserves injected into the system as the starting amount.
Excess reserves
Excess reserves = deposits − required reserves
Required reserves = deposits × reserve requirement. Only excess reserves can be lent.
Equation of exchange
M × V = P × Y
V is velocity. Quantity theory assumes V and Y are stable, so P moves with M.
Functions of money
Medium of exchange; unit of account; store of value
Know which function a scenario describes.

How to solve Money: Functions, Creation and Money Multiplier questions

Use the same sequence for any question on money, reserves or the equation of exchange.

  1. 1Identify what is asked: a function of money, a definition (narrow or broad), a multiplier, or a change in money supply or prices.
  2. 2Write down the reserve requirement as a decimal, or list the variables M, V, P and Y.
  3. 3For a multiplier question, compute 1 ÷ reserve requirement.
  4. 4Multiply the multiplier by the new reserves or excess reserves to get the maximum change in deposits or money supply.
  5. 5For equation of exchange questions, hold the stated variables constant and solve for the unknown using M × V = P × Y.
  6. 6Check for leakages: excess reserves or cash held by the public lower the actual multiplier.
  7. 7Eliminate the two options that reverse the direction or confuse the function, then confirm the last one.

Quickest way: Multiplier in one line

When to use it: Any numerical question giving a reserve requirement and an initial injection of reserves.

  1. Divide 1 by the reserve ratio to get the multiplier.
  2. Multiply by the injection to get the maximum increase in deposits.
  3. For the equation of exchange, convert to growth rates: %ΔM + %ΔV ≈ %ΔP + %ΔY.
  4. Pick the option that matches; numerical options run smallest to largest, so check the order for errors.

Common mistakes in Money: Functions, Creation and Money Multiplier

  • Multiplying by the reserve requirement instead of dividing 1 by it.

    Students mix up the multiplier with the required reserve amount.

    Fix: A smaller reserve ratio must give a bigger multiplier. Use 1 ÷ ratio and sanity-check that result.

  • Applying the multiplier to total deposits rather than new reserves.

    The multiplier is remembered, but the base is not.

    Fix: Apply it to the new reserves or excess reserves injected, not to the whole existing deposit base.

  • Treating the simple multiplier as the real-world result.

    Textbook examples ignore leakages.

    Fix: Remember that excess reserves and cash held by the public reduce the multiplier. The simple formula gives a maximum.

  • Confusing narrow money with broad money.

    Both are called money supply.

    Fix: Narrow is notes, coins and demand deposits. Broad adds savings, time deposits and similar near-substitutes.

  • Mixing up the functions of money.

    Scenarios describe behavior, not the label.

    Fix: Paying for a purchase is medium of exchange. Quoting prices is unit of account. Holding wealth for later is store of value.

  • Forgetting that quantity theory needs V and Y to be stable.

    The equation is an identity, but the theory adds assumptions.

    Fix: State the assumption before concluding that money growth equals inflation.

Worked examples

Example 1

The reserve requirement is 8%. A central bank injects €200 million of new reserves into the banking system. Assuming no excess reserves and no cash held by the public, what is the maximum increase in the money supply?
A. €1,600 million
B. €2,500 million
C. €25,000 million

Show the solution
  1. Reserve requirement = 0.08.
  2. Money multiplier = 1 ÷ 0.08 = 12.5.
  3. Maximum increase = €200 million × 12.5 = €2,500 million.
  4. Option A multiplies by 8 (200 × 8 = 1,600) instead of dividing 1 by 0.08. Option C is a decimal slip: 200 × 125 = 25,000, which comes from using 1 ÷ 0.008 instead of 1 ÷ 0.08.

Answer: B. €2,500 million

Example 2

In an economy, money supply grows 6%, velocity is constant and real output grows 2%. Using the equation of exchange, what is the approximate change in the price level?
A. 2%
B. 4%
C. 8%

Show the solution
  1. M × V = P × Y, so %ΔM + %ΔV ≈ %ΔP + %ΔY.
  2. 6% + 0% = %ΔP + 2%.
  3. %ΔP ≈ 6% − 2% = 4%.
  4. Option C comes from adding output growth to money growth (6% + 2% = 8%) instead of subtracting it. Option A is just the output growth rate.

Answer: B. 4%

Exam tips

  • Questions often give a reserve ratio and a deposit. Compute the multiplier first, then check which base to use.
  • Expect conceptual items asking which function of money a situation illustrates. Match the behavior to the function.
  • Remember that the simple multiplier is a maximum. Options mentioning leakages usually point to a smaller real multiplier.
  • For equation of exchange items, use growth rates and keep track of the sign of each term.
  • With no penalty for wrong answers, never leave a question blank. Eliminate the option that reverses the direction first.

Practice questions from Monetary Policy

Money: Functions, Creation and Money Multiplier in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Money: Functions, Creation and Money Multiplier: frequently asked questions

What is the money multiplier formula in CFA Level I?

The simple money multiplier is 1 ÷ reserve requirement. With a 20% reserve requirement, the multiplier is 5. It gives the maximum expansion of deposits per unit of new reserves.

What is the difference between narrow money and broad money?

Narrow money is the most liquid money: notes, coins and demand deposits. Broad money adds less liquid items such as savings and time deposits and similar assets. Definitions vary by country.

How does fractional reserve banking create money?

Banks keep a fraction of deposits as reserves and lend the rest. The borrowed money is spent and redeposited, which lets other banks lend again. Each round creates new deposits, so the money supply grows by a multiple of the initial reserves.

What does the quantity theory of money say?

It uses M × V = P × Y. If velocity and real output are stable, changes in the money supply lead to proportional changes in the price level. This is why monetarists link inflation to money growth.