Banks keep only a fraction of their deposits as reserves and lend out the rest, and those loans create new money. Use Part A to run one bank's balance sheet move by move, then use Part B to follow a deposit through many banks and see why the total levels off at excess reserves times the money multiplier.
Every number on this page is a hypothetical teaching number. These problems use the limited-reserves model, where the required reserve ratio limits how much banks can lend.
A bank keeps only part of its deposits as reserves (vault cash plus its deposit at the Fed) and lends the rest. When a loan is spent and redeposited at another bank, that bank can lend again. This chain is how the banking system creates money.
Assets go on the left: reserves, loans, and securities. Liabilities and owner's equity go on the right: demand deposits and the owners' capital. Deposits are a liability because the bank owes them to customers. Every move changes the two sides by the same amount, or swaps one asset for another.
Required reserves = required reserve ratio × demand deposits. Excess reserves = total reserves − required reserves. A single bank can safely lend only its excess reserves.
The money multiplier is 1 divided by the required reserve ratio. With a 10% ratio it is 10. The maximum change in the money supply = excess reserves × money multiplier (for a Fed purchase from the public, add the initial deposit, which is itself new money). Do not mix it up with the spending multiplier, 1/MPS.
Depositing cash you already had does not change the money supply at first: currency just turns into a checkable deposit. Only the new loans add money. When the Fed buys bonds from the public, it pays with brand-new money, so the deposit itself is new money and counts too.
The simple multiplier assumes banks lend every dollar of excess reserves and every loan comes back as a deposit. When banks hold extra reserves or people hold some cash, less is relent each round, so the actual multiplier is smaller than 1/rr.
These are the patterns AP questions use. Cover the right-hand columns and try each row yourself. "First bank" means the bank that receives the deposit or sells the bond.
| Event | Ratio | Required reserves (first bank) | Excess reserves (first bank) | Max new loans, one bank | Multiplier | Max change in money supply |
|---|---|---|---|---|---|---|
| Customer deposits $1,000 of cash she already had | 10% | $100 | $900 | $900 | 10 | +$9,000 ($900 × 10) |
| Fed buys $1,000 of bonds from the public; seller deposits the payment | 10% | $100 | $900 | $900 | 10 | +$10,000 ($1,000 + $900 × 10) |
| Fed buys $1,000 of bonds from a bank | 10% | $0 change (deposits did not change) | $1,000 | $1,000 | 10 | +$10,000 ($1,000 × 10) |
| Business deposits $500 of cash it already had | 20% | $100 | $400 | $400 | 5 | +$2,000 ($400 × 5) |
| Fed buys $2,000 of bonds from the public | 25% | $500 | $1,500 | $1,500 | 4 | +$8,000 ($2,000 + $1,500 × 4) |
| Customer withdraws $1,000 in cash (bank had no excess reserves) | 10% | Falls by $100 | Short by $900 | Must cut loans by $900 | 10 | Up to −$9,000 ($900 × 10) |
| Fed sells $1,000 of bonds to the public (banks had no excess reserves) | 10% | Falls by $100 | Short by $900 | Must cut loans by $900 | 10 | Up to −$10,000 ($1,000 × 10) |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 4.4. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 4 terminology guide.