Deposit Expansion Step by Step: How $1,000 Becomes $10,000#

Someone walks into a bank and deposits $1,000 in cash. A few weeks later, the banking system holds $10,000 in total deposits — ten times the original amount. Nobody counterfeited anything. No printing press ran overtime. No laws were broken. Yet the money supply expanded by $9,000 that didn’t previously exist. The explanation isn’t magic. It’s arithmetic.

Setting the Stage#

Before tracing the journey of that $1,000 deposit, two ground rules. First, assume a reserve requirement of 10%. Every bank in the system must hold at least 10% of its deposits as reserves and can lend out the remaining 90%. Second, assume every dollar lent by one bank eventually gets deposited into another. No cash leaks out of the system. Nobody stuffs bills under a mattress.

These are simplifications. Reality introduces friction, delays, and leakage at every stage. But the stripped-down model reveals the core mechanism with crystalline clarity, and the complications layer in naturally once you see the skeleton. You have to understand the bones before the muscles and skin make sense.

The key number: the money multiplier — 1 divided by the reserve ratio. At 10%, the multiplier is 10. That number represents the theoretical maximum expansion of the money supply from a single injection of base money. The journey from $1,000 to $10,000 is the multiplier in motion.

Step 1: Bank A Receives the Deposit#

The depositor places $1,000 into Bank A. The balance sheet shifts immediately. On the liability side, the bank now owes the depositor $1,000 — a demand deposit, withdrawable at any time. On the asset side, it holds $1,000 in cash reserves.

Bank A must retain 10% as required reserves: $100. The remaining $900 is excess reserves — funds the bank is free to lend. Holding excess reserves earns almost nothing. Lending them out earns interest. The incentive structure is clear.

Bank A approves a $900 loan to a small business owner. At the moment the loan is issued, the bank credits the borrower’s account with $900. This is money creation happening in real time. The original depositor still has $1,000 in the bank. The borrower now has $900. Total deposits at Bank A: $1,900. The money supply just grew.

But the borrower didn’t take a loan to watch a number sit in an account. That $900 gets spent — paying a supplier, buying equipment, covering payroll. The money flows out of Bank A and into the broader system.

Step 2: Bank B Enters the Chain#

The supplier who received the $900 payment deposits it at Bank B. Now Bank B mirrors the pattern: $900 in new deposits, 10% ($90) locked up as required reserves, and $810 in excess reserves ready for lending.

Bank B lends $810 to another borrower. That borrower spends it. The money flows to yet another recipient, who deposits it at Bank C.

Watch the numbers. The original $1,000 generated a $900 loan. That $900 generated an $810 loan. Each round is exactly 90% of the previous one — a geometric sequence with a common ratio of 0.9. This pattern isn’t random. It’s mathematically inevitable given the 10% reserve requirement.

Step 3: Bank C and the Shrinking Cascade#

Bank C receives $810 in deposits. Holds $81 in reserves. Lends $729. The borrower spends the $729, and it lands at Bank D.

Bank D gets $729. Holds $72.90. Lends $656.10. On and on it goes.

Each step is smaller than the last — like ripples spreading from a stone dropped into still water. The initial splash is dramatic. By the tenth ripple, you can barely see it. By the hundredth, it’s imperceptible. But every ripple adds to the total displacement.

By round five, cumulative new deposits reach $4,095.10. By round ten, $6,513.22. The numbers climb toward a ceiling but never quite reach it in any finite number of steps. They approach it asymptotically — getting infinitely close without ever arriving.

The Mathematical Proof#

Total deposits from this process form a geometric series:

Total Deposits = $1,000 + $900 + $810 + $729 + $656.10 + …

This is the sum of an infinite geometric series with first term $1,000 and common ratio 0.9. The formula:

Total = First Term ÷ (1 - Common Ratio)

Total = $1,000 ÷ (1 - 0.9) = $1,000 ÷ 0.1 = $10,000

The reserve ratio is 0.1. The multiplier is 1 ÷ 0.1 = 10. The original $1,000 generates $10,000 in total deposits. Of that, exactly $1,000 ends up as total reserves (10% at each bank), and $9,000 exists as loans that created new deposits.

The math is exact — not an approximation or an estimate. Given the assumptions — a uniform 10% reserve requirement, no cash leakage — the result is as certain as 2 + 2 = 4.

The Beauty of Geometric Decay#

Something remarkable hides in these numbers. Each successive round contributes less to the total. The first five rounds account for roughly 41% of the final $10,000. The first ten rounds cover about 65%. Reaching 90% of the total takes approximately 22 rounds. Reaching 99% takes about 44.

This pattern — rapid initial growth that gradually tapers off — shows up everywhere in nature and mathematics. Radioactive decay follows the same curve. So does the cooling of a hot object. The banking system’s deposit expansion echoes a universal mathematical structure.

The decay is also what keeps the system stable. If each round produced the same amount as the previous one, the total would be infinite. The 10% reserve requirement ensures each round is strictly smaller, guaranteeing convergence to a finite sum. The constraint isn’t merely regulatory. It’s mathematical necessity.

What the Numbers Obscure#

For all its clarity, the step-by-step model hides several important realities. First, the process doesn’t happen sequentially. Banks don’t wait in line for the previous bank to finish lending. Thousands of banks lend and receive deposits simultaneously, in a continuous flow rather than a tidy chain.

Second, the model assumes every dollar lent returns to the banking system as a deposit. In practice, some cash stays in circulation. People hold physical currency. Businesses keep cash on hand. This cash leakage shrinks the effective multiplier. If 5% of each loan leaks out as cash, the multiplier drops from 10 to roughly 6.7.

Third, the model assumes banks lend their maximum allowable amount. In reality, banks frequently hold excess reserves beyond the required minimum, especially during uncertain times. After the 2008 crisis, U.S. banks accumulated trillions in excess reserves, pushing the actual multiplier far below its theoretical ceiling.

These complications don’t invalidate the model. They refine it. Consider a striking real-world example: in April 2026, Customers Bank announced a deal with OpenAI to deploy AI in its lending operations, compressing loan approval timelines from 30–45 days down to just seven (CNBC). Faster approvals mean faster deposit creation — each round of the multiplier cycle completes in days rather than weeks, accelerating the cascade that turns one deposit into many. The core mechanism — lending creates deposits, deposits enable more lending, in a diminishing cascade — holds. The complications explain why the real-world multiplier is typically smaller than the theoretical maximum.

The Key Realization: No Single Bank Creates 10x#

Here’s the most important insight, and it contradicts popular mythology. No single bank in this chain creates $10,000 from $1,000. Bank A creates $900 in new money. Bank B creates $810. Bank C creates $729. Each individual bank lends only a fraction of the deposits it receives, fully within the rules.

The multiplication is a system-level phenomenon. It emerges from money circulating through multiple institutions, each performing the same simple operation: hold reserves, lend the rest. No individual actor does anything extraordinary. The extraordinary result — a tenfold expansion — arises from the collective repetition of an ordinary act.

This distinction matters for understanding both responsibility and risk. When critics accuse banks of “creating money from nothing,” they attribute to individual institutions a power that belongs only to the system as a whole. A single bank is a conduit. The system is the amplifier.

From Macro to Micro#

The step-by-step model presents deposit expansion from the perspective of the entire banking system — a bird’s-eye view tracking money as it flows from institution to institution. But what does this look like from inside a single bank? What actually changes on the balance sheet when a deposit arrives, when a loan goes out, when the money leaves?

Shifting from macro to micro doesn’t change the math. It changes the understanding. The system-level multiplier is the sum of many individual decisions, each governed by the same rules but experienced differently by each participant. A bank receiving a deposit doesn’t see itself as step 37 in a geometric series. It sees a new liability, a new asset, and a lending opportunity.

The next chapter moves inside the walls of a single bank to watch the balance sheet shift in real time — a deposit arriving, a loan departing. The multiplication that seems almost magical from the outside turns out to be entirely mundane from the inside. Which is precisely the point.