Am I missing something?
Here is a scenario:
Imagine total of
BTC1000 in actual currency exists...
Alfred owns all of it an deposits this
BTC1000 into an on demand checking account at a bank.
(Total bank deposits
BTC1000, Total bank loans
BTC0, Reserve on hand
BTC1000, Reserve 100%)
Betty receives a loan from the bank of
BTC800.
(Total bank deposits
BTC1000, Total bank loans
BTC800, Reserve on hand
BTC200, Reserve 20%)
So the bank has loaned out a "fraction" of their deposits, not a "multiple" of their deposits.
Betty uses the
BTC800 to purchase something from Charlie
Charlie deposits the
BTC800 that he just received from Betty into his own checking account.
(Total bank deposits
BTC1800, Total bank loans
BTC800, Reserve on hand
BTC1000, Reserve 55%)
Notice the
BTC1800 in deposits at the bank from
BTC1000 currency limit. This is how "fractional reserve" multiplies money.
Notice the bank still only has
BTC1000 in reserve on hand. There is no increase in the actual amount of bitcoins in existence, but if you add up how much each individual thinks they have, the total is greater than the
BTC1000 limit. Meanwhile, nobody believes they have accepted a bitcoin backed banknote, since they can all see that they've actually received real bitcoins that they deposited at the bank. Lets carry the process forward and see what happens.
Denise receives a loan from the bank of
BTC640. (re-loaning out the same money that was already loaned out to Betty, and deposited by Charlie)
(Bank deposits
BTC1800, Bank loans
BTC1440, Reserve on hand
BTC360, Reserve 20%)
Denise uses the
BTC640 to purchase something from Elliot
Elliot deposits the
BTC640 that he just received from Denise into his own checking account.
(Bank deposits
BTC2440, Bank loans
BTC1440, Reserve on hand
BTC1000, Reserve 41%)
Francine receives a loan from the bank of
BTC512. (re-loaning out the same money that was already loaned out to Betty and Denise)
(Bank deposits
BTC2440, Bank loans
BTC1952, Reserve on hand
BTC488, Reserve 20%)
Francine uses the
BTC512 to purchase something from George
George deposits the
BTC512 that he just received from Francine into his own checking account.
(Bank deposits
BTC2952, Bank loans
BTC1952, Reserve on hand
BTC1000, Reserve 34%)
Hanna receives a loan from the bank of
BTC409. (re-loaning out the same money that was already loaned out to Betty, Denise, and Francine)
(Bank deposits
BTC2952, Bank loans
BTC2361, Reserve on hand
BTC591, Reserve 20%)
Hanna uses the
BTC409 to purchase something from Ivan
Ivan deposits the
BTC409 that he just received from Francine into his own checking account.
(Bank deposits
BTC3361, Bank loans
BTC2361, Reserve on hand
BTC1000, Reserve 30%)
At this point we already have
BTC3361 in deposits from that single
BTC1000. Alfred, Charlie, Elliot, George, and Ivan all believe that they are the true owners of this money since they each received real bitcoins and then deposited it into their own checking account. Where did the extra
BTC2361 come from? Meanwhile the bank has re-loaned out the same money over and over without a single cent of it having been repaid yet. The bank's "fractional reserve" never fell below 20%, and yet somehow they've managed to loan out "multiple of its reserves".
This process can continue over and over, expanding the money supply until there is
BTC5000 in deposits, since the maximum the bank can ever have in reserve is the full
BTC1000 of physical cash in existence. This would result in
BTC5000 in deposits,
BTC4000 in outstanding loans waiting on repayment, and
BTC1000 in reserves.