they simply create a $100 credit of new money in your account, whilst at the same time debiting you $100 in a new payment request. From the bank's point of view there has been no net change; their reserves haven't changed and their balance book still has the same bottom line. However, $100 of new money has just been created
Accounting rules may be different across the world
But where I live (Russia), the net balance (the balance book in your speak) gets increased by the amount borrowed. The reason for that is simple. The money thus created increases both assets and liabilities of the bank as the credit (which is the bank's asset) gets credited (yeah) to the borrower's account (this deposit then becomes the bank's liability), and the bottom line necessarily gets augmented. It also makes sense as the bank is typically offered some form of collateral. In this manner, it is not quite correct to speak of this money as printed out of thin air because technically it is a collateralized form of money
We just create a supply of money out of thin air and expect everyone else to work for it? ahh sounds like $lavery, oh not to mention now you have to pay interest on that $100 that does not even exist compound or not
It is not that simple, either. The money is still created based on demand for credit, while the latter should be secured by enough collateral (well, at least in theory). So it is not like a bank can print money nonstop 24/7. No honey, no money