A lot of people misunderstand what creating money means in the context of fractional reserve banking. Banks "create money" every time they make a loan backed by a deposit. They're not literally creating new money. This is how it works:
- Alice deposits $100 into the bank. The bank owes Alice $100.
- Bob wants a loan. The bank offers him a loan of $50, backed by the $100 from Alice. The bank owes Alice $100. Bob owes the bank $50.
- Bob withdraws the $50 to spend on coke and hookers. The bank uses $50 of the money deposited by Alice to give to Bob. Bob has $50. Alice still has $100 balance.
The bank has just created $50. Everyone is happy unless Alice (and everyone else) wants to withdraw their money and they aren't able to get it back from Bob. That's a bank run.
All money in the bank is created by the bank. When you deposit $100 of physical cash (money) into the bank, the bank creates a $100 bank deposit (also money) and holds $100 of physical cash (money) in its vault. There is now $200 of money.
The bank may buy a government bond with it. In that case there's $100 of physical cash (money) that the government has, a $100 government bond (also money) that the bank has, and a $100 bank deposit (also money) that you have. There is now $300 in total.
Stacking money on top of money is fundamental to the economy. Normally (and enforceably in cryptocurrency systems) the different layers may not be confused, nor may different assets at the same stacking level. But it benefits whoever is creating the higher layers when you confuse them with the lower layers. When people widely bank deposits with base money, this benefits the banks because now the money they print becomes almost as good as base money. When people widely confuse government bonds with base money, this benefits the treasury because now the money they print becomes almost as good as base money. If people were to widely confuse Apple stock with base money, it would benefit Apple and its existing investors.
(Base money doesn't have to be gold by the way. It's anything that's issued without underlying value and widely accepted as a store of value. Fed notes serve as base money just fine. They have about as much actual real-world value as gold bars, which is none.)
Another way to see it is that physical $100 has $300 of value.
But eventually, Alice wants her money back, the bank cashes in the bond, the government repays the cash.
So part of that value is the value of trust as a function of time. Trust in the bank, trust in the government, trust that they'll pay back their debts on a defined schedule. Plus interest.
What's even more funny is that in modern times the required asset to debit ratio is only 10%.
So in your example, the bank can lend $1000 to Bob, backed by Alice's $100.