September 10, 2019 Tuesday
Bedtime Story
Series of Fractional-Reserve Processing Leads to a Geometric Series
This money that gets deposited now in other
bank in turn undergoes processing through the same fractional-reserve system in
other commercial banks where a fraction of it is kept back and rest lent out.
This cycle then continues.
It is also well known and understood that
not all the money that has printed circulates in this manner as people have a
tendency to hoard money both in the form of cash and unaccounted gold/foreign
currencies/digital currencies with themselves.
Businesses try their utmost to minimize
paying income taxes; in the United States the IRS identifies small businesses
and sole proprietors as the largest group of tax evaders simply because there
are very little ways to know their non-reporting of incomes without spending excessively
on investigations.
The most common modality of tax evasion in
the United States is to overstate the contributions made to charity especially
to churches (Religion is everywhere, there is simply no escaping from it).
These cycles of fractional-reservations and
lending of the rest allows the money to increase in a geometric series.
Geometric series results in the growth of
monetary supply in the economy via geometric progression which you know is the
sequence of numbers where each term after the first is obtained by multiplying
the previous one by a fixed, non-zero number.
This fixed multiplier is known as the
common ratio.
For instance the sequence of numbers 1, 5,
25, 125 … is a geometric series whose common ratio is 5.
Similarly 25, 5, 1, 0.2, 0.04 … is a
geometric series whose common ratio is 1/5.
The general formula for a geometric series
for a fixed common ratio r is:
a, ar, ar2, ar3, ar4,
…
Here the letter ‘a’ represents a number
which is known as the scaling factor which is also the starting value of the
series.
Of course it is understood that for a
geometric series the number ‘r’ can never be equal to zero.
The letter ‘r’ and its value is most
important in deciding how the geometric series will behave.
If the value of the letter ‘r’ lies between
-1 and +1 but not zero then the series will head towards exponential decay.
But the greatest dividend comes when the
value of the common ratio is greater than 1; in such a case the sequence will
show exponential growth towards positive infinity if the sign of the initial
value of a is positive.
In markets and finance both the compound
interest and Ponzi schemes rely on the exponential growth for their success and
lucre.
The counter-intuitiveness of exponential
growth through geometric progression has been well demonstrated by two
classical mathematical problems:
Stay tuned to the voice of an
average story storytelling chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
Advertisements
Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
No comments:
Post a Comment