Deposit $100 in a bank. It keeps a fraction in reserve and lends the rest out; that loan gets spent and re-deposited, and the next bank lends most of IT, and so on. One real $100, at a 10% reserve, ends up backing $1000 of money in the system. Banks don’t print money — lending multiplies it. Slide the reserve ratio and watch the cascade.
Under fractional-reserve banking, a deposit D with reserve ratio r lets the bank lend (1−r)D; that loan is re-deposited, the next bank lends (1−r)²D, and so on — a geometric series D·Σ(1−r)ⁿ that sums to D/r. So $100 at r = 10% supports $1000 of deposits; the money multiplier is 1/r. It is why central banks steer the economy through reserve requirements and rates, and why bank lending — not the printing press — creates most money. A fail-loud self-check throws unless the cascade sums to exactly 1/r. ◆ real monetary economics, node-verified.
The textbook 1/r multiplier (the exact geometric sum); in practice banks are constrained by capital and demand, not just reserves, and some systems have no reserve requirement — the re-lending-multiplies-money mechanism and its 1/r ceiling are exact.