That’s not really how it works. The bank takes savings deposited and issues most of it as loans keeping enough on hand to issue to people withdrawing their savings (fractional reserve banking). The interest on the loans pays the interest on the savings (which is why one tracks the other). They also borrow money from the markets (or the central bank) at low interest rates to reissue as higher-interest loans. Nowhere in that system do they create money out of thin air or send money to /dev/null (although I get the impression they do some of that in derivatives markets).
Actually, the GP's explanation is closer to true than yours is. I was taught the same explanation you gave, but it doesn't fit the facts on the ground. Banks don't base the loans they issue on deposits (the closest to this they come are the capital requirements regulators impose on them), they base them on models of the borrower's ability to repay and on models of the ability to resell the loan (aka 'securitization', though less so since that practice helped drive the financial crisis). If the models fit, the loan amount is credited to the seller, and debited to the buyer, essentially creating money 'out of thin air.' The economist Steve Keen is perhaps one of the more vocal advocates of this view (http://www.debtdeflation.com/blogs/).
This is how the system works. There's a limit to that practice (the money multiplier), which is one of the reasons why banks need to rotate money as you said (another being cross-bank transfers). See this link:
https://en.wikipedia.org/wiki/Money_creation#Credit_theory_o...
Mortgages make MBS, mortgaged backed securities, which are traded around. You can buy these, or SLABs, student loan backed securities.
Neither are money. M0 money can only be made by the US Fed. M1 or M2 money can be made by banks out of savings accounts or checking accounts, due to the fractional reserve system.
By lending money to a bank through the savings account mechanism, the bank owes YOU money, because the bank spends roughly 80% of it on other things.
That's why there is a distinction from M0 pure cash, and the M1 or M2 virtual 'nearly money' in the system. I think credit cards are a higher order of money as well...
