[Lafclaria]

This thread is fraught with errors. In the original example, there's no reference to the deposits that the bank has on hand, which critical to the discussion. So let's start over:

Amy is an artist who sells paintings, and has a $1000 surplus which she deposits in Angus Bank. To understand, we'll assume that this is all the money in the world. We're also going to assume that Amy gets about 0% interest on her deposit, which is sadly realistic.

Under a fractional reserve system requiring 10% reserve (which is variable, but let's keep it simple), Angus Bank is allowed to loan out all but 10%. So they lend $900 to Builder Bob at 10% annual interest. Bob's not ready to invest the money yet in his construction project, so he deposits it in Beta Bank.

Amy has $1000 in demand deposit. [+1000]
Angus Bank has a $1000 liability to Amy, plus $100 in reserve., plus a $900 asset in the money that Bob is going to pay back. They didn't really "create" the $900; it's money that Amy gave them. So they are neutral [+0]
Bob has a $900 demand deposit at Beta Bank. But he owes $900 to Angus Bank. [+0]
Beta bank has a $900 liability owed to Bob, plus $900 in reserve. [+0]

So in terms of net value, it remains at $1000. However, the "M1 money supply" is Amy's demand deposit ($1000) plus Bob's deposit ($900). This is the amount of liquid assets available for withdrawing and spending. (The money in bank reserve can't be spent, because it must remain in reserve to meet the fractional requirement). So in this sense, the available spending money supply has been increased out of thin air. But it required Amy's initial cash deposit, which she created by being productive.

Now Beta Bank loans $810 to Chef Charlie at 10% interest rate, keeping $90 (10%) in reserve. Charlie deposits the money in Cantina Bank.

Then a year goes by. Now:

Amy has $1000 deposited in Angus Bank. [+1000]
Angus Bank has $100 in reserve, plus a $1000 liability to Amy, plus a $900 asset from Bob, plus Bob owes $90 in interest. [+90]
Bob owes $900 to Angus Bank, and he owes them $90 interest, and he has a $900 deposit with Beta Bank. [-90]
Beta Bank has $90 in reserve, plus a $900 liability to Bob, plus a $810 asset from Charlie, plus Charlies owes $81 interest. [+81]
Charlie owes $810 to Beta Bank, and he owes them $81 interest, and he has a $810 deposit with Cantina Bank. [-81]
Cantina bank has $810 in reserve, an $810 liability to Charlie [+0]

So the net value in the system remains +1000.

But the spendable/loanable money supply not "trapped" by reserve requirements is:
Amy's $1000 deposit
Angus Bank's $90 interest.
Bob's $900 deposit.
Beta Bank's $81 interest.
Charlie's $810 deposit.

This totals to $2881. You can see if this process were to continue, the money "created" would be the interest owed to the banks when it is repaid, but the supply of money to grease the economy would be much greater than that. Brought to its extreme limit, it could increase the money supply by 10x of Amy's original earned $1000. So the increase in the money supply is much greater than the money "created". But remember, there's still only $1000 in FRNs to support the whole system.

The next lesson would be how the loaned money unwinds...