You could lend $9,000. Ideally you put it into an account at your bank where now you have $19,000 on deposit and $9,000 on loan. Now you can loan an addition $8,100. Then you can loan $7,290. Then you can loan $6,561. Etc. Sum up all those loans. The initial $10,000 causes the creation of far more than $9,000. It works the same way if there is more than one bank involved, as in that case it is "the banking system" creates all the new money in total, rather than just one bank where the initial deposit was made.
Yay! this is actually coherent enough to address!
So the reason what you write sounds so obviously unsound, is you are only writing about HALF of a banking system.
Loans are barter. I give you something. You give me something.
When I loan someone $9,000 I take something worth $12,000 as collateral. That assures that the borrower has at least 30% "skin in the game". If his idea sucks, he loses more than he borrowed. Now that gives me two ways to win. If he pays me back, I get interest. If he doesn't pay me back, I claim the collateral and sell it. Think of it as loan insurance. It is what real bankers do instead of showing up and breaking the borrowers knee caps. It may be less fun, but it is more profitable.
If you look around, you will see lots of disreputable lenders offering collateralize loans they know people are "overly optimistic" about paying back. Pawnshops are an easy example. The same is done with use car loans.
Now, when the business man puts his $9,000 in my bank its because he needs to pay bills over time. He knows they will come up, but he doesn't need to spend the money now. He may not have to spend it at all if he has sufficient cash flow.
And when I lend that money out again, it's because I do have real value backing that loan. In this case collateral is a very valuable "claim check". If they don't pay, I claim the house, car, company, gold, tools, etc.
So I lend $8,100 and take $11,000 in collateral. If that person deposits the money with me, I can do it all again.
I have the money, its all cash. None of it was made up or came from the Fed.
If someone comes in and want more cash than I have on had, I can go to any other bank for a loan. I can use my collateral as collateral on that loan. It is perfectly sensible to do so.
If everyone requests their cash at once, all my collateral assets get pledged to other banks who happened to have more cash on hand. And that is still perfectly sensible. Because I now have no risk. I paid all my depositors off. The other banks have the risk so they hold the collateral.
Or I can simply sell my loans to an outside investor. They are investments guaranteed by collateral. And the best thing is, as the loan gets paid back the borrower's "skin in the game" increases. Since they have more to lose, they will work harder to make all payments. Who wants to lose a car for missing the last car payment?
Notice, in no case did I go running to the Fed. In most banking transactions the Fed is not required at all.
Where the fed is needed is when all your cash is out on loan, but there is still more opportunity to grow the economy.
Say I did your progression. I lent out all that money and took gobs and gobs more in collateral. Everything is going smoothly, people are making payments. But now I have no cash on hand available to loan.
Now say Fred comes in and has a great business ideal. He also has collateral to back the loan. The problem is I have no cash. So in this case I go to the bank where I can borrow money the cheapest. (sometimes the fed but most banks can't borrow there directly) So I borrow money, and pledge his collateral to back my loan. I do the paperwork, charge him more interest than the fed charges me. Everyone gets paid back.
There is no magic and no scamming.
Unless you SUCK AT BANKING! Which has happened recently. It is not a scam, it is a bunch of fucking morons who failed to do proper risk assessment or take proper collateral. They should all be lined up and SHOT for sucking so much at their one and only job. Most of the fault actually lies with so called "investors" who created a market by purchasing sets of prepackaged loans, without knowing what the fuck they were doing! It is really easy to create and run a hugely profitable business if you customers are fucking morons! And most of the "investors" who bought the loans were fucking morons. They'll claim the guys who packaged up the unvetted loans scammed them. But it is easy to scam a fucking moron.
By the way, EVERYTHING I wrote works for fractional reserve bitcoin or gold lending as well.
Stick that in your FAQ. :-)
Or you could use the $10,000 as collateral to borrow from the central bank. They will give you $100,000 to loan out.
This is unsupported. I doubt it is true. Central banks and/or collateral simply doesn't work like that.
Feel free to support this point if you want.
Of course, all those numbers assume a 10% fractional reserve. Currently in the U.S. the reserve requirement for savings accounts, certificates of deposit, etc. is 0% and for checking (demand) accounts it is 3%. (Read the fine print on your savings account, they are required to warn you that withdrawals might be denied until convenient for the bank up to typically 30 days.)
Changes in reserve percentages don't effect anything I said. If you have more cash on hand you lose the value that comes from lending it. But you save on time consuming interbank transactions to manage cash levels.