How to Calculate the Money Multiplier
The money multiplier equals 1 divided by the required reserve ratio; multiply it by new excess reserves to find the maximum change in the money supply.
The Money Multiplier formula
Calculator
Enter the reserve ratio and a new deposit to get the money multiplier and the maximum money creation.
Share of deposits banks must hold. Enter 10 for 10% (0.10).
The fresh deposit that lands in the banking system.
$900 of excess reserves can become as much as $9,000 of new deposits. The real figure is smaller because banks hold extra reserves and the public keeps some cash.
- Money multiplier
- 10
- Required reserves on the deposit
- $100
- Excess reserves
- $900
Each $1 of excess reserves supports up to $10 of new deposits.
The deposit minus the reserves required against it. This is what the bank can lend out.
How to calculate Money Multiplier, step by step
- 1Find the required reserve ratio. The fraction of deposits banks must hold (e.g., 10% = 0.10).
- 2Compute the multiplier. Money multiplier = 1 ÷ reserve ratio.
- 3Find excess reserves. New deposit minus required reserves on that deposit.
- 4Multiply. Maximum change in money supply = money multiplier × excess reserves.
Worked example: Money Multiplier
With a 10% (0.10) reserve ratio, the money multiplier = 1 ÷ 0.10 = 10. A $1,000 deposit creates $900 in excess reserves, which can expand the money supply by up to 10 × $900 = $9,000.
Multiply excess reserves, not the deposit
This is the mistake that costs the most marks. The multiplier acts on the reserves a bank is free to lend, not on the whole sum that walked in the door. A $1,000 cash deposit at a 10% ratio leaves $100 locked up as required reserves and $900 free, so lending can create at most 10 × $900 = $9,000 of new deposits.
Check it the other way to be sure. Total deposits end up at 1,000 + 9,000 = $10,000, which is exactly the original $1,000 divided by the 0.10 ratio. Both routes agree, and if your two answers disagree you have almost certainly multiplied the deposit rather than the excess.
Read the question carefully for which figure it wants. "The maximum increase in the money supply" and "the maximum increase in demand deposits" usually mean the $9,000 that lending created. "Total deposits in the banking system" means the $10,000.
An open market purchase is not the same starting point
When the central bank buys $1,000 of bonds directly from a bank, no customer has made a deposit, so there are no required reserves to set aside against one. The full $1,000 arrives as excess reserves, and the maximum expansion is 10 × $1,000 = $10,000 rather than $9,000.
The difference of $1,000 is small, and it is exactly the sort of thing an exam uses to separate students who applied a formula from students who understood it. Ask where the money landed. Reserves created out of nothing by the central bank are all lendable; reserves that arrived attached to a customer deposit are not.
Why the real multiplier is nowhere near 1 ÷ rr
The simple formula assumes every dollar lent comes straight back as a deposit and every bank lends out everything it legally can. Neither holds. Households keep some of what they receive as cash, and banks hold reserves beyond the requirement.
Currency held by the public does the most damage. Writing c for the ratio of cash to deposits, the multiplier becomes (1 + c) ÷ (rr + c). At a 10% reserve ratio the simple formula gives 10, but a currency ratio of 0.10 cuts it to 5.5, and a ratio of 0.25 cuts it to 3.6. A small habit of holding cash roughly halves the effect.
The formula with c in it is beyond what AP asks you to compute, so treat it as the reason behind the standard exam sentence rather than something to memorise: the actual expansion falls short of the maximum because currency in circulation and excess reserves are both leakages out of the lending chain.
Money Multiplier questions
Why is the real-world money multiplier smaller?
Banks may hold excess reserves and the public holds some cash instead of depositing it, both are leakages that shrink the actual multiplier.
How is it different from the spending multiplier?
The money multiplier expands the money supply through bank lending; the spending multiplier expands GDP through re-spending of income (1 ÷ (1 − MPC)).
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