How to Calculate Maximum Deposit Expansion
Maximum deposit expansion equals excess reserves multiplied by the money multiplier, which is 1 divided by the required reserve ratio.
The Deposit Expansion formula
Calculator
Enter a new deposit and the reserve ratio to see what one bank can lend and what the whole system can create.
The fresh deposit that lands in the banking system.
Enter 20 for 20%, which the calculator reads as 0.20.
As the loan is spent and redeposited, the system can create up to $4,000 of new loans and new deposits. Real expansion falls short because banks sit on reserves and people keep cash.
- Money multiplier
- 5
- Required reserves on the deposit
- $200
- What this one bank can lend
- $800
- Total checkable deposits in the system
- $5,000
1 divided by 0.2 gives 5, so every $1 of excess reserves can support $5 of deposits.
Held against the new deposit and never lent out.
The bank that took the deposit can write loans of $800, its own excess reserves, and not a dollar more.
The original deposit plus everything lending creates. Watch the wording: this total is larger than the $4,000 of newly created deposits.
How to calculate Deposit Expansion, step by step
- 1Identify what the problem gives you. Check whether you are handed new excess reserves or a new deposit, because the two lead to different totals.
- 2Strip out required reserves. If a deposit is given, required reserves = ratio × deposit, and the remainder is excess reserves.
- 3Build the multiplier. Money multiplier = 1 ÷ required reserve ratio.
- 4Multiply. Maximum new loans and newly created deposits = excess reserves × the multiplier.
- 5Match the answer to the wording. Total checkable deposits in the system reach deposit × the multiplier, while newly created deposits leave out the original deposit.
Worked example: Deposit Expansion
A customer deposits $1,000 in cash and the problem uses an illustrative required reserve ratio of 20% (0.20). Required reserves = 0.20 × $1,000 = $200, so excess reserves = $800 and the multiplier = 1 ÷ 0.20 = 5. The banking system can create up to $800 × 5 = $4,000 in new loans and new deposits, taking total checkable deposits to $1,000 + $4,000 = $5,000. The bank that received the deposit can still lend only its own $800.
Deposit Expansion questions
Why do some answers use deposit × the multiplier instead?
Both appear on the exam: deposit × the multiplier is the final total of checkable deposits, while excess reserves × the multiplier is the amount newly created by lending.
Does the money supply rise by the full expansion?
Not when the deposit was cash already in circulation, since that currency left M1 as it entered the bank. The net rise in the money supply is then the newly created deposits alone.
Why is the real expansion smaller than the maximum?
Banks that sit on excess reserves and households that keep cash out of banks are both leakages, so lending stops short of the theoretical maximum.
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