Fractional Reserve Banking: Deposit Multiplier Simulator

Regulatory Reserve Ratio

Required reserve ratio r 10%

Interest Rates

Loan rate (earned) 6.0%

Deposit rate (paid) 1.5%

Lending Chain

System Readouts

Money supply created

$100,000

Deposit multiplier 1/r

10.0×

System reserves held

$10,000

Net interest / round

Reserve requirement (min 10%): compliant

How it works

An initial deposit D₀ = $100,000 arrives at Bank 0. Under a required reserve ratio r, the bank must hold back a fraction r as reserves and may lend out the rest. That loan is spent and redeposited at the next bank, which repeats the process:

Reserve at bank n:  Rₙ = Dₙ · r
Loan at bank n:     Lₙ = Dₙ · (1 − r)
Next deposit:        D₍ₙ₊₁₎ = Lₙ = Dₙ · (1 − r)

Total money supply after N rounds:
  M = D₀ · [1 − (1 − r)^(N+1)] / r

As N → ∞:  M → D₀ / r   (the deposit multiplier m = 1/r)

Each geometric term (1 − r)ⁿ shrinks the deposit at every step, but the sum of every deposit ever created is larger than D₀ — this is how a fractional-reserve banking system expands the money supply from a single deposit. A lower reserve ratio means a larger multiplier and faster money creation; regulators set a reserve-requirement floor (shown here as a 10% minimum, historically the U.S. Federal Reserve's standard) precisely to cap how far this chain can run.

Step — advances the chain by one bank, computing its reserve/loan split and feeding the loan to the next bank as a new deposit.
Auto-run — steps automatically until the chain reaches its visible limit.
Loan / deposit rate — every bank in the chain earns interest on its loan book and pays interest on its deposit book; the net interest margin readout sums that spread across every active bank, showing how narrower reserve ratios also multiply interest income (and risk) system-wide.

Banks active: 1

Reserves held Loaned out Money in transit

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