I'm trying to create a math blog, and I just happened to explore a topic that both interests me as well as the general audience (many blockchain enthusiasts). Most people here dislike the banking system (hence, why they are cryptotoken users).

The purpose of this post was to illustrate money multiplication via reserve rates and demonstrate how infinite geometric series can be applied to my understanding of the system at that time.

My illustration may have been a poor example to what happens in the real world, but whether banks borrow from the central bank in order to meet RR before a loan is made or after a loan is made does not change the underlying principle of how money multiplication, via deposits in a bank.

So, yes, one could have instead simply used the (inverse of 1 - RR) - 1 and expressed this as the maximal money multiplier that could have occurred and stated that the actual MM is determined by numerous factors, including a ratio of how much of a particular loan is kept in cash, not used to pay off other businesses, and is therefore not deposited into a new bank account. And in fact, you'll note that I do state that is the maximal MM that can exist and indeed derive it from using the infinite geometric series model. Coincidence?

I could do a completely new post that explains this in light of all the new economics that I have learned from @sigmajin and yourself, if you think it would prove worthwhile.