Why interest-bearing loans do not create an ever-increasing demand of money

I sometimes hear it claimed that the practice of charging interest causes an ever-increasing demand for money. The argument goes, since principal plus interest is more than principal alone, money needs to be created (by taking on a new loan) in order to pay back the loan. It is then claimed that this creates a vicious circle of ever-mounting debt. The argument is fallacious and demonstrates a fundamental misunderstanding of the nature of money. If, as is indeed the case, money can be reused, there is no vicious circle. Consider the following gedanken experiment.

Suppose I loan you twelve twenty-euro notes for one year, with principal repayment every month and interest totalling twenty euros due at maturity (that is, at the end of the year).

For simplicity, let’s assume you do nothing with the money, just sit on it. Every month you come to me and give me one of the notes I loaned you.

Assume for simplicity again that I do not do anything with the notes I receive from you, I just sit on them.

At the end of the year, you have one twenty-euro note and an obligation to pay me fourty euros (the last installment of principal, plus the agreed interest). What do you do?

One thing you could do is come to me and ask for a further loan. That could be done, I could give you one of my hoarded twenty euro notes and you could then retire the original debt (albeit with a new twenty-euro debt). But this is not the only option.

Another option is that you mow my lawn a couple of times. The wage we agree on is fourty euros in total (assume for simplicity that there are no taxes etc). You do the work, I give you two of my hoarded twenty-euro notes; you now have sixthree of them, one left from my loan and two that I paid you with. Now you can pay the last installment of the principal and the interest. End result: you are no longer in debt, and you have a twenty-euro note that you can do whatever you want with.

Neither scenario required the creation of new money.