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RE: The Mathematics of Fractional Reserve Banking
Ok, let's try this: why do you need limits to describe something that can be expressed as a simple percentage?
Ok, let's try this: why do you need limits to describe something that can be expressed as a simple percentage?
Because it is a deeper analytical method of mathematics that can be used to understand the subject and in fact you need limits to really understand how an infinite geometric series really operates.
Yeah, the "loaners/sellers" wasn't meant as a quote or anything, it's just the simplified concepts my brain uses to try understand all this :)
Ok, I get your point. I'm not nearly as good in math as you, and much less in translating math to English. I was hoping to do what you suggested and write one (3?) articles about this. However, I can't get it working in my head... See this post, feedback highly appreciated. Same for our friend @sigmajin
https://steemit.com/steemit/@r4fken/fractional-reserve-banking-and-steemit-questions-for-experts
Yes, you need limits for infinite series. Not for percentages. It feels like a farfetched look-how-smart-i-am post.
Also, the assumption that loaners pay and sellers just deposit again is flawed.
I don't see how percentages would get point across of money multiplication as well as how this model (albeit, imperfectly) fits with an infinite geometric series.
This is an example I've used in my Calculus II courses numerous times when introducing infinite geometric series and sequence.
Can you provide an example of how percentages describe this phenomena?
In response to the loaners and sellers comment ... I never used the terminology of sellers and loaners, so it looks like you're interpreting that I said certain statements that I did not?
Maybe you could provide a quote or an example with some more meat on the bone to back up what you are claiming that I said.
OK. I think I see what you mean by loaners and sellers (although, as I said, that terminology was not used).
For all practical purposes of understanding the situation, assume that any loan that a bank gives to 1 contractor goes to one other business. In reality, the loan goes to pay for employees, business expenses to multiple businesses, stays on hand for petty cash, etc. However, at the end of the day, the vast majority of the capital winds up back in the banks.
Even if 80% is re-deposited back into banks, you still have money multiplication, just not at the extreme end if 100% was re-deposited. See @sigmajin's example where some of the cash was kept on hand from various businesses.
For the purpose of instruction, aggregating totals of payments of a business into a single entity (when the practical mathematics are the same) is easier to explain the mathematics of an infinite geometric series.