In one sentence, this animation illustrates your misconception about "They can only lend money they have in deposits. Technically, they can in fact lend money they don't have, but they will have to close this imbalance as soon as possible..."
First off, at the banker's counter you see two balancing rows of people; 1. adding money to a deposit and 2. borrowing money from the bank. All's well and sound. Yet, those were the old days and that situation complies to "our" common sense about a bank's process. Nowadays though, when a starter needs money, he goes to a bank where the banker gives him credits by filling in numbers in a computer. The bank's safe actually is (almost) empty (2% liquidity is no exception). So in fact the bank created money it did not possess merely by typing a number in a computer. This virtual number gets in the starter's briefcase and is spread into the market; invisible (non-existing) coins are everywhere and people treat them as if they are real. In times of crises however the whole imaginarium falls to pieces and the debt-relay ends at the tax-payers; those are your 4X.
This is likely what most people think about banks "creating money out of the thin air". And this is obviously not what money multiplication is all about in reality. If the shown animation (or your description of it) had any semblance with reality, banks could create assets without balancing them with corresponding liabilities (this would make the whole idea of FRB null and void)...
Jumping in here. Money is base money plus credit, to the degree that the credit is transferable. Let me give a basic example.
Suppose a friend wants to sell a car. You want to buy it, but you don't have money. You make a deal that you pay later. Now your friend has a claim for money on you, and you have the goods. Next your friend wants to buy something from
his friend. He says, I want that, but I have no money. But my other friend owes me, and when he pays, I can pay you. That is even if he has no money, he can spend the credit, and in case of saving he can also be assured that he has sufficient value saved for the future, without actually having the base money.
He has only a claim. Even in this informal situation, money has been created from nothing in the form of credit, and it can be used for indirect exchange just as base money. The situation can be formalized as a bill of exchange, which change hands just like money. When the loans are paid back, this extra money disappears, but you can easily imagine that the procedure can be repeated immediately when the bill is cleared. So credit is money. There is no multiplication, there was nothing, then there was money. That is money creation.
Actually, you create money
derivatives in the form of bills of exchange, bank receipts, IOUs, or whatever other kinds of claim...
But why are you telling
me all this in the first place? I know this perfectly well and can say it even simpler. When you have a claim on me, you have an asset
which you can just sell to the third party and get the money you need. But as a bank you needn't actually sell your claim (unless there is a bank-run) since it is a liquid asset which is considered as money, increases the balance and pays you interest. But
every asset out there is balanced with a liability in this and every other case, so I would hardly call it "creating money out of the thin air", because for the most people (as can be seen from the above animation) it means creating assets (since money is an asset too) out of nowhere without at the same time being balanced by corresponding liabilities...
And this is what is called money multiplication, i.e. creating mutually extinguishing assets and liabilities
