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That might have been true long ago but with fractional reserve lending this linkage is effectively severed. The bank usually isn't lending out your money. The total amount a bank can lend out is constrained more by regulatory requirements and its invested capital than by the balance of customer savings/checking/CD accounts.

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It's true that the lending amount of a bank is heavily constrained by regulatory requirements. But that doesn't mean that banks are not lending your deposited money to someone else.

Consider two banks in the same country, so having to comply with the same reserve requirements. The reserve requirements are defined as a percentage of the amount on the banks's deposit account at the central bank. So the bank which can transfer an extra deposit to this acount is the one which is able to lend more money.

And what, would you say, is the current legally mandated "reserve requirement" in the US?

https://www.federalreserve.gov/monetarypolicy/reservereq.htm

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