Banks Actually Create Money
Here's a sentence that sounds wrong but is true: commercial banks create money when they make loans. The Fed alone doesn't control how much money exists in the economy. The Fed sets the reserves; banks then multiply those reserves into a much bigger money supply through lending. Section 4.4 is the math of that multiplication.
If the Fed adds $1 billion of reserves to the banking system through an open-market purchase, the eventual increase in the money supply is much more than $1 billion. With a 10% reserve requirement, the answer is up to $10 billion. With a 20% reserve requirement, up to $5 billion. The exact amount depends on the money multiplier, and getting that calculation right is one of the most heavily tested skills in Unit 4.
This section builds in three layers. First, we'll meet fractional reserve banking — the system that makes money creation possible in the first place. Second, we'll learn to read a bank's balance sheet (or T-account), which is how AP exam questions actually present this material. Third, we'll work through the money multiplier formula step by step, with a hyperspecific focus on the AP exam's favorite trap: the difference between what a single bank can lend and what the entire banking system can create.
📝 Why this section often shows up as a full FRQ: Recent AP exams have featured FRQs where every part is built around the money multiplier — a customer deposits cash, then you compute the change in liabilities, change in required reserves, maximum loans by a single bank, and finally the maximum change in MS for the whole banking system. Getting fluent with both calculations is the difference between full points and missing 4+ points on a single FRQ.
Fractional Reserve Banking: The Foundation
In the US (and every modern banking system), banks operate under fractional reserve banking. The defining feature: when you deposit money in a bank, the bank doesn't just hold all of it in the vault waiting for you to withdraw it. The bank keeps a small fraction in reserve and lends out the rest.
Fractional Reserve Banking: A system in which banks are required to hold only a fraction of their customer deposits as reserves, lending the rest out to other borrowers. This is what enables the banking system to create money through lending — and is the central feature the AP exam tests under "what does a commercial bank's ability to create money depend on?"
Here's why this matters. If a bank held 100% of every deposit (a "full reserve" system), then $1 deposited would only ever be $1 of money. Banks would just be storage lockers. But under fractional reserve banking, your $1 deposit lets the bank lend $0.90 (with a 10% reserve requirement) to someone else. That $1 in your checking account and the $0.90 in the borrower's pocket are both money. The same dollar of reserves is now backing more than $1 of money supply. Multiply this across thousands of banks and millions of deposits, and you get the modern money supply.
🎯 AP exam test point: A frequent multiple-choice question asks: "A commercial bank's ability to create money depends on which of the following?" → The correct answer is always "a fractional reserve banking system." Memorize this exact phrasing — it's a free point.
Reading a Bank's Balance Sheet (T-Account)
AP exam questions on the money multiplier almost always come with a T-account — a simplified balance sheet shaped like a "T" with assets on the left and liabilities on the right. You need to know what goes on which side and how to spot excess reserves at a glance.
Assets
Liabilities
What Goes Where, and Why
The logic is easy once you flip your perspective from the customer's viewpoint to the bank's:
- Assets (left side) — things the bank owns or things owed to it. Cash in the vault and reserves at the Fed (both required and excess) are assets. Loans the bank has made to customers are also assets — because customers owe the bank that money. Government securities (bonds) the bank holds are assets too.
- Liabilities (right side) — things the bank owes. The biggest item is demand deposits — your checking account is a liability to the bank because the bank owes you that money on demand.
Here's the counterintuitive part: your checking account is the bank's liability, not its asset. From the bank's perspective, it owes you that money. From your perspective, it's an asset. T-accounts always show things from the bank's point of view, so deposits appear on the right.
The Two Big Calculations from a Balance Sheet
Whenever the AP exam gives you a T-account, you'll typically need to compute one or both of these:
Required Reserves = Demand Deposits × Reserve Requirement (rr)
If deposits are $100,000 and rr = 10%, required reserves = $10,000.
Excess Reserves = Total Reserves − Required Reserves
If total reserves are $15,000 and required reserves are $10,000, excess reserves = $5,000.
Identifying Excess Reserves
Bank B has $100 in actual reserves and $600 in demand deposits. The reserve requirement is 10%. How much can Bank B increase its loans?
That last point is the single most important rule on this entire topic, and it appears in every AP exam: a single bank can lend out an amount equal to its excess reserves — no more, no less. Anything beyond excess reserves would violate the reserve requirement.
Required vs. Excess Reserves — The Key Distinction
The whole money-multiplier story hinges on the difference between two types of reserves. Mix them up and you'll get every related question wrong; understand them and you'll get them all right.
Required Reserves
Definition: The minimum amount banks must hold against deposits, set by the reserve requirement.
Formula: Demand Deposits × rr
Can be lent out? NO. These are by law not available for lending.
Role in multiplier: Determines how much each round "leaks" out of the lending chain.
Excess Reserves
Definition: Reserves above the required minimum that the bank could lend if it chose to.
Formula: Total Reserves − Required Reserves
Can be lent out? YES. These are the bank's "lending capacity."
Role in multiplier: The starting point. Only excess reserves get multiplied.
When a Customer Makes a Cash Deposit
This is the exact scenario that appears on FRQs over and over. Walk through what happens at the depositing bank when you deposit $1,000 in cash, with a 10% reserve requirement:
- Liabilities ↑ by $1,000 — the bank now owes you $1,000 (your demand deposit).
- Total Reserves ↑ by $1,000 — the bank now has $1,000 of cash in its vault.
- Required Reserves ↑ by $100 — 10% of the new deposit is locked up.
- Excess Reserves ↑ by $900 — the rest is available to lend.
- Maximum new loans for this single bank: $900 — exactly equal to the new excess reserves.
Assets
Liabilities
⚠️ Important: A cash deposit does NOT initially change M1. The cash was already counted in M1 as currency in circulation. After the deposit, it becomes part of M1 as checkable deposits instead. Different category, same total — until banks start lending out the new excess reserves, at which point the multiplier kicks in and M1 begins to grow. This is exactly the "common exam trap" from 4.1.
How Banks Create Money — The Round-by-Round Process
Let's trace what happens to a $1,000 cash deposit across the entire banking system, not just one bank. Assume a 10% reserve requirement, no excess reserves held back, and every borrower redeposits 100% of their loan into another bank.
| Round | New Deposit | Required Reserves (10%) | Lent Out (New Money) | Running Total of New Money |
|---|---|---|---|---|
| 1 | $1,000.00 | $100.00 | $900.00 | $1,000 |
| 2 | $900.00 | $90.00 | $810.00 | $1,900 |
| 3 | $810.00 | $81.00 | $729.00 | $2,710 |
| 4 | $729.00 | $72.90 | $656.10 | $3,439 |
| 5 | $656.10 | $65.61 | $590.49 | $4,095 |
| … | … | … | … | … |
| ∞ | $10,000 | $1,000 | $9,000 | $10,000 |
The initial $1,000 cash deposit eventually expands to $10,000 total in the money supply. The banking system created $9,000 of new money through lending. What's "magical" here isn't really magic — it's that the same dollar of reserves is now backing 10× the demand deposits, because each time the money is redeposited, only 10% has to be set aside.
Why the Total Equals 10×
This is a geometric series: 1,000 + 900 + 810 + 729 + … The mathematical formula for an infinite geometric series with ratio r is sum = first term / (1 − r). Here the ratio between consecutive terms is 0.90 (because 10% leaks out each round). So the sum is $1,000 / (1 − 0.9) = $1,000 / 0.1 = $10,000. The fraction 1 / 0.1 = 10 is the money multiplier.
Money Multiplier = 1 / rr
If rr = 10% → multiplier = 10. If rr = 20% → multiplier = 5. If rr = 25% → multiplier = 4. If rr = 5% → multiplier = 20.
🎯 Quick memory check: The smaller the reserve requirement, the bigger the multiplier. A 5% rr → 20× multiplier; a 25% rr → 4× multiplier. This is exactly why lowering the reserve requirement is expansionary — it makes the multiplier bigger.
The Three Formulas You Must Know Cold
These three formulas handle every money-multiplier question on the AP exam. Memorize them, practice them, and don't confuse them with each other.
Money Multiplier = 1 / rr
The maximum multiplication factor for the banking system.
ΔMSmax = (1 / rr) × ΔExcess Reserves
Maximum total change in money supply for the banking system.
ΔLoansmax (banking system) = ΔMSmax − Initial Deposit
or equivalently:
ΔLoansmax = (Multiplier − 1) × ΔExcess Reserves from the deposit
Maximum total new loans created across the banking system.
Maximum Change in Money Supply
The Fed buys $500 worth of bonds from a commercial bank, adding $500 in excess reserves to the banking system. The reserve requirement is 20%. What is the maximum change in the money supply?
Initial Cash Deposit, Banking System Multiplication
Maggie deposits a $100 cash gift into her checking account. The reserve requirement is 10%. Banks hold no excess reserves and all loan proceeds are redeposited. What is the maximum increase in total money supply?
⚠️ Cash deposit vs. Fed bond purchase — the subtle difference: Both add reserves to the banking system, but a cash deposit moves money that's already in M1 from one form (currency) to another (deposits) — so the multiplier amplifies the change net of that initial reshuffle. A Fed bond purchase adds brand new reserves that weren't in M1 yet. AP FRQs are picky about this distinction — read the prompt carefully. If a customer deposits cash, the answer to "maximum change in MS" is typically the multiplied amount of the excess reserves only, not the full deposit × multiplier.
Single Bank vs. Banking System — The AP Exam's Favorite Trap
This is the most-missed concept in Section 4.4, and it shows up in nearly every FRQ that uses the multiplier. Read carefully: the question almost always asks two separate things, and you need different answers for each.
A Single Bank
"How much can this one bank lend?"
Answer: Only its excess reserves. No more.
Formula: Max new loans = Excess Reserves of this bank only.
Why: A single bank can't multiply — once it lends out the loan, that money goes to another bank as a deposit. The first bank can only do its piece of the chain (round 1).
Numerical example: $1,000 cash deposit, rr = 10% → single bank can lend up to $900.
The Entire Banking System
"How much can the money supply change?"
Answer: Excess reserves × money multiplier.
Formula: ΔMSmax = (1 / rr) × ΔExcess Reserves.
Why: The whole system can multiply — Bank 1's loan becomes Bank 2's deposit, which lets Bank 2 lend, which becomes Bank 3's deposit, and so on across all banks.
Numerical example: Same $1,000 cash deposit, rr = 10% → entire system can create up to $9,000 in new money ($10,000 total MS including the original deposit's reclassification).
🎯 The two-step FRQ pattern: "Maggie deposits $100 in cash... (b) What is the maximum new loan ABC Bank can make from her deposit? (c) What is the maximum change in the money supply throughout the entire banking system?" Two different answers from the same deposit. Part (b) = $90 (excess reserves of ABC Bank). Part (c) = $900 ($90 × 10 multiplier). Don't put the same number twice.
The Full FRQ Pattern
Lucy deposits $40,000 in cash at ABC Bank. The reserve requirement is 5%, and the banking system has limited reserves. (Adapted from a recent AP FRQ.)
(a) Change in ABC Bank's liabilities?
(b) Change in required reserves?
(c) Maximum new loans ABC Bank can initially make?
(d) Maximum change in MS for the entire banking system?
Why the Multiplier Doesn't Always Reach Its Maximum
The formulas above give the maximum change. In real life, the actual change is usually smaller. The AP exam tests three reasons why the multiplier underdelivers:
- Currency drains. If borrowers don't redeposit 100% of their loans — if they keep some as cash — then less money flows back into the banking system for the next round of lending. The chain gets shorter.
- Excess reserves held by banks. If banks choose to hold some of their excess reserves without lending them out (especially common when interest rates are low or risks feel high), then not every dollar of excess reserves gets multiplied. This was a huge issue after the 2008 financial crisis — banks held massive amounts of excess reserves rather than lending.
- Lack of credit-worthy borrowers. Even if banks want to lend, they need customers willing and able to borrow. In a deep recession, demand for loans may dry up.
Actual ΔMS ≤ Maximum ΔMS. The multiplier formula gives an upper bound. The AP exam recognizes this — that's why FRQ questions often say "maximum change in money supply" rather than just "change in money supply." If the question says "maximum," use the full formula. If it doesn't specify, you may need to mention that the actual change could be smaller due to leakages.
Common Misconceptions
Section 4.4 is the most calculation-heavy section in Unit 4. These misconceptions are the difference between getting full points and partial credit.
- "A single bank can multiply deposits using the multiplier formula." No. A single bank can only lend out its own excess reserves. The multiplier formula applies to the entire banking system across multiple lending rounds. If a question asks about one bank, the answer is just excess reserves; if it asks about the whole system, then apply the multiplier.
- "Required reserves can be lent out." No — required reserves are by definition the amount banks cannot lend. Only excess reserves are available for lending. Mixing these up is the most common balance-sheet error.
- "A cash deposit immediately increases M1." Not initially. The cash was already in M1 as currency in circulation. After deposit, it's in M1 as checkable deposits instead. M1 is unchanged until banks start lending out the new excess reserves, at which point the multiplier creates additional money.
- "The money multiplier is rr." Backward — the multiplier is 1/rr. With rr = 10%, the multiplier is 10, not 0.1.
- "Bigger reserve requirement means more money creation." Backward. A bigger reserve requirement makes the multiplier smaller, so less money gets created from each dollar of reserves. Lower rr → bigger multiplier → more money creation.
- "Loans are liabilities of the bank." No — loans are assets of the bank (someone owes the bank money). The corresponding deposit is the liability.
- "Deposits are assets of the bank." Also wrong. From the bank's perspective, deposits are liabilities — the bank owes that money to the customer. (It's confusing because deposits are assets from your perspective as the customer.) On a bank's T-account, deposits always appear on the right.
- "The maximum change in MS is the same as the maximum new loans." Subtle but tested. For a cash deposit, the maximum change in MS is multiplier × excess reserves, but the maximum new loans is (multiplier − 1) × excess reserves, because the original deposit isn't itself a loan. Read AP questions carefully — they sometimes ask one and sometimes the other.
- "If the Fed sells $20 million in bonds, MS decreases by exactly $20 million." No — MS decreases by up to $20 million × the multiplier. With a 25% reserve requirement, multiplier = 4, so MS could fall by up to $80 million. Always apply the multiplier when the Fed's action ripples through the banking system.
- "Banks create money by printing it." No — physical money is printed by the government's mint. Banks create money by making loans. When a bank credits $1,000 to your account in exchange for your promise to repay (a loan), that $1,000 is new money. No printing required.
⚡ 4.4 Quiz: 5 Questions
Click an answer to lock it in. Every option gets a full breakdown — what's right, what's wrong, and the AP-favorite trap each distractor is designed to catch.
1. Assume the reserve requirement is 20%. If a bank initially has no excess reserves and $10,000 cash is deposited in the bank, the maximum amount by which this single bank may increase its loans is:
✓ Correct answer: (B)
Note the key phrase: "this single bank". The single-bank limit is its excess reserves, not the system-wide multiplier total. Work through it:
The bank now has $8,000 it can lend without violating the reserve requirement. If it lent more, it would dip into required reserves, which is not allowed.
Why the other options miss the mark
- (A) $2,000 is the change in required reserves, not the lending capacity. Required reserves can't be lent.
- (C) $10,000 is the full deposit. A bank can't lend out the entire deposit — it has to set aside 20% as required reserves first.
- (D) $20,000 isn't related to any standard calculation here. Possibly a confusion with money multiplier × something else.
- (E) The "banking system" trap — this looks like the multiplier result (5 × $10,000 = $50,000), but the question is about one bank, not the system.
🔗 Review: Re-read "Single Bank vs. Banking System." The rule of thumb: single bank → excess reserves only; entire system → excess reserves × multiplier.
2. Assume the required reserve ratio is 10%, banks hold no excess reserves, and all loan proceeds are redeposited. If $100 in cash is deposited into a checking account, the maximum increase in the total money supply across the banking system is:
✓ Correct answer: (C)
The full chain: the $100 was already in M1 as currency, so depositing it doesn't itself change M1. What changes M1 is the new lending the banking system can do based on the new excess reserves.
The $900 represents brand new money created by the banking system through loans.
Why the other options miss the mark
- (A) $100 is the original deposit only. This ignores the multiplier effect across the banking system entirely.
- (B) $800 is incorrect arithmetic — possibly confusing the formula. The right multiplier with rr = 10% is 10, not 8.
- (D) $1,000 forgets that the original $100 cash was already part of M1. Only the new money from lending counts as an increase.
- (E) $1,100 has no basis in the standard calculation — possibly a guess.
🔗 Review: Walk through Worked Example 3 in the Formulas section. The cleanest framing: "Maximum new money = excess reserves × multiplier" — don't include the original cash deposit, since it was already counted in M1.
3. ABC Bank is a commercial bank in Country X. Assume the required reserve ratio is 25% and banks in Country X keep no excess reserves. If ABC Bank sells $20 million worth of government bonds to Country X's central bank, what will happen to the money supply after all adjustments are made in the banking system?
✓ Correct answer: (C)
Read carefully: ABC Bank sells bonds TO the central bank. That means the central bank is buying bonds (an open-market purchase) — which is expansionary. The central bank pays ABC Bank with newly created reserves, giving the banking system more reserves to lend out.
Why the other options miss the mark
- (A) $5 million is incorrect arithmetic — possibly the result of dividing by the multiplier instead of multiplying. The right answer is excess reserves × multiplier, not divided.
- (B) Reversed direction. The central bank is buying, which is expansionary, not contractionary.
- (D) Wrong direction. The dollar amount ($80M) is correct, but the direction is backward — this is an expansionary purchase from the Fed's side, so MS rises.
- (E) $500 million doesn't match any reasonable calculation. Possibly a confusion with $20M × 25 or similar arithmetic error.
🔗 Review: Cross-reference with Section 4.3 — when the central bank buys bonds (no matter who is selling), it's expansionary. The multiplier then determines how much MS rises across the system: 1/rr × ΔExcess Reserves.
4. A bank has $800 million in demand deposits and $100 million in total reserves. The reserve requirement is 10%. The bank's excess reserves equal:
✓ Correct answer: (D)
Excess reserves equal total reserves minus required reserves. Work through it step by step:
The bank could lend out up to $20 million without violating the reserve requirement.
Why the other options miss the mark
- (A) $10 million doesn't match standard arithmetic. Possibly arose from dividing total reserves by 10, ignoring deposits entirely.
- (B) $80 million is the required reserves ($800M × 0.10), not excess. This is the most common wrong answer.
- (C) $100 million is total reserves, not excess reserves. Excess reserves are only the portion above the required minimum.
- (E) $200 million isn't reachable from the given numbers.
🔗 Review: Re-read the two key formulas: Required Reserves = Deposits × rr, then Excess Reserves = Total Reserves − Required Reserves. Practice computing both whenever you see a T-account.
5. Which of the following is the defining characteristic of a fractional reserve banking system?
✓ Correct answer: (B)
The defining feature of fractional reserve banking — and the entire reason banks can create money — is that banks hold only a fraction of customer deposits as reserves. The rest gets lent out, creating new deposits at other banks, which can then lend out part of those, and so on. The "fractional" part is exactly what makes the money multiplier work.
If banks had to hold 100% of deposits as reserves (full reserve banking), they'd just be storage lockers. The money supply could never expand beyond the monetary base, and the multiplier would equal 1.
Why the other options miss the mark
- (A) A central bank is a separate institution. Fractional reserve banking can exist without a central bank (and historically often did). The defining feature is the fraction held as reserves, not the existence of a central bank.
- (C) This describes the gold standard / commodity money, which is a different concept from fractional reserve banking. Fiat money systems can also be fractional reserve.
- (D) 100% reserve banking is the opposite of fractional reserve banking. This is the most common wrong answer — students misread "fractional" as somehow related to "fraction = 1" rather than "fraction less than 1."
- (E) Deposit insurance (in the US, the FDIC) is a separate institution that protects depositors against bank failures. It's important but not the defining feature of fractional reserve banking.
🔗 Review: Re-read "Fractional Reserve Banking: The Foundation." Lock in: "A commercial bank's ability to create money depends on a fractional reserve banking system." This phrasing is exactly what AP graders look for.
Ready for more? Take the full Unit 4 Practice Test →
End of Section 4.4. Up next: 4.5 The Loanable Funds Market — the second key graph in Unit 4, where the real interest rate is determined and where crowding out happens.