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Definition of ‘Multiplier Effect’
The expansion of a country's money supply that results from banks being able to lend. The size of the multiplier effect depends on the percentage of deposits that banks are required to hold as reserves. In other words, it is money used to create more money and is calculated by dividing total bank deposits by the reserve requirement.
Investopedia Says
Investopedia explains ‘Multiplier Effect’
The multiplier effect depends on the set reserve requirement. So, to calculate the impact of the multiplier effect on the money supply, we start with the amount banks initially take in through deposits and divide this by the reserve ratio. If, for example, the reserve requirement is 20%, for every $100 a customer deposits into a bank, $20 must be kept in reserve. However, the remaining $80 can be loaned out to other bank customers. This $80 is then deposited by these customers into another bank, which in turn must also keep 20%, or $16, in reserve but can lend out the remaining $64. This cycle continues - as more people deposit money and more banks continue lending it - until finally the $100 initially deposited creates a total of $500 ($100 / 0.2) in deposits. This creation of deposits is the multiplier effect.
The higher the reserve requirement, the tighter the money supply, which results in a lower multiplier effect for every dollar deposited. The lower the reserve requirement, the larger the money supply, which means more money is being created for every dollar deposited.
You said: ...so If I make a $100,000 loan then the bank only needs to have $10 k actually, they create the 90,000 $ out of thin air to give me the 100k loan.
This is as wrong now as it was when you first posted it. If you want to borrow $100,000 from the bank, they'd better have $100,000 (+ 10% of $100,000) in deposits, or they won't be loaning you $100,000. The bank can't create any money out of thin air. The money they lend has to be deposited.
No bank can loan out 500% of the deposits they hold.
Look, 2 deposits, $100 and $80, two loans, $80 and $64. Every loan funded by a larger deposit. If a bank could really create money out of thin air, why would they need a deposit, ever?