The language used to describe fractional reserve is pretty misleading. Banks don't increase the total supply of money, all fraction reserve does is keep more of it in circulation. If a bank takes a $1,000,000 deposit one customer, and lends $850,000 of it to other customers, there isn't $1,850,000 worth of money all of a sudden. There is $850,000 worth of debt held by customers, and another customer with a $1,000,000 balance, which on the banks books will be represented by $150,000 or cash reserves and that $850,000 of debt.
The thing that seems to confuse people is the abstraction mechanism by which the $1,000,000 depositor doesn't see any of the $850,000 debt, and the by which they can withdraw the $1,000,000 without being involved in any debt transactions themselves. Fractional reserve banking doesn't create money out of thin air, it's just a system that allows for deposits to be put to productive use. The alternative is that deposits are entirely withdraw from the economy completely until the depositor wants to use them, which would be the economic equivalent of hoarding all your money under the mattress.
The rest of it also doesn't really "go to the bank", it's money that they must have on hand to service withdrawals, and absorb defaults and other losses.
The thing that seems to confuse people is the abstraction mechanism by which the $1,000,000 depositor doesn't see any of the $850,000 debt, and the by which they can withdraw the $1,000,000 without being involved in any debt transactions themselves. Fractional reserve banking doesn't create money out of thin air, it's just a system that allows for deposits to be put to productive use. The alternative is that deposits are entirely withdraw from the economy completely until the depositor wants to use them, which would be the economic equivalent of hoarding all your money under the mattress.
The rest of it also doesn't really "go to the bank", it's money that they must have on hand to service withdrawals, and absorb defaults and other losses.