- 4009 - COMPOUND INTEREST - most important math you will ever learn. It not only affects you personally it tells you how to understand the world:
- 4009 - COMPOUND INTEREST - most important math you will ever learn?
- We
will start with your refinancing your mortgage.
It is 5% fixed for 30 years. To learn how soon you will double the
amount of your loan in interest simply divide 5% into the number 70. 70 / 5
= 14 years.
-
- In 14
years from the start you will have paid double your loan. Will your home double in price in 14
years? Let’s say you pay $200,000 to the
builder, if that is the amount of your loan you pay another $200,000 to the
banker in 14 years, and he did not even get his hands dirty.
-
- The
formula is simple. It is : Interest rate
* years = 70
-
--------------------------------------- i *
t =
70
-
- Let’s
say you just read that we will double our national debt in 10 years. What rate of growth is the spending exceeding
revenue?
-
---------------------------------- 70 / 10 years
= 7% per year.
-
- The
deficits added to the debt each year is growing at 7% per year. Is inflation growing that fast? Is productivity growing that fast? Are taxes increasing that fast?
-
- Where
does this math come from? Growth rates
and compound interest are an exponential function . The function is the slope of an exponential
curve where something has constant growth over time.
-
- The
curve is the function e^(i*t), the i*t
is the exponent and we simply take the logarithm to find the value of the
exponent. OK, that is too esoteric. Here it is again:
-
----------------------- 70
= 100 log to base “e” of 2
-
---------------------- 70
= 100 ln 2
-
----------------------- ln 2
= 0.693147
-
- We
multiply by 100 because we are using percentage for interest or growth
rates. 69 is close to 70. 70 is easier to divide with. But, you can use the number 69 if you want to
be more exact. ln 2 is the natural log
of doubling a quantity.
-
-
Let’s say the population growth is increasing at 2% per year. How soon will it double? We have a world population today of 7 billion.
-
------------------- 70 / 2%
= 35 years.
-
- In 35
years, in the year 2046 the population will be 14 billion unless we lower the
growth rate.
-
- This
math can work in amazing ways that should be easy for you to calculate:
Let’s say you want to save some money for
Christmas shopping. You set a piggy bank
on the kitchen counter and start by contributing 1 penny on December 1st. You are determined to double your
contribution every day to go shopping on Christmas Eve. Here is how it will work
-
--------------------------------------------------- Pennies ------ Pennies
-------------------------------------------------- Contribution --- Total
-
--------------
0 ------------- December 1
--------- 1 ------------ 1
-
--------------
1 ------------- December 1
--------- 2 ------------- 3
-
--------------
2 ------------- December 1
--------- 4 ------------- 7
-
--------------
3 ------------- December 1
--------- 8 ------------- 15
-
--------------
4 ------------- December 1
--------- 16 ------------ 31
-
-
-
--------------
x ------------- December x +1
----- 2^x ----- 2^(x+1) -1
-
-
-
--------------
23 ------------- December 24
------ 2^23 ---------- 2^24 -1
-
--------------
23 ------------- December 24
------ $83,886 ----- $117,772
-
- You
can see that doubling every day is the same as 2 raised to the number of
days. The first day is zero.
-
- So on
the 23 day, Christmas Eve you have to contribute $86,886 to the piggy
bank. You may have to have borrowed that
from the Chinese.
-
- Also
note that the next day’s contribution is the amount 1 more than the previous
day’s total: 3+1 =
4, 7 + 1 =
8, 15 + 1 = 16, 2^(x+1) -1 is always the next total. On December 24 your will have $117,772 in the
piggy bank. Congratulations you have
over $100,000 to spend on Christmas. I
hope I am on your Christmas list.
-
- This
last point says that if the consumption of oil doubles every 10 years then the
amount consumed in this decade is more than all the previous decades
combined. The U.S. per capital
consumption of resources is 30 times greater that those living in developing
countries.
-
- We
have an obligation to become more efficient.
To conserve more. To develop
alternative energy sources. It is in the
math. What we are doing and spending is
unsustainable. An announcement will be
made soon, stay tuned.
-
- Using
the formula : interest * time = 70 when doubling. We are doubling every day. Therefore the interest rate per year is
4,783% per year. If you get a piggy bank
that can collect that fast, Keep IT!!!
-
-
Thinking is hard, it tends to be very upsetting. But, the facts do not go away when you ignore
them. We would rather embrace what is false because it is more comforting. The chief cause of problems is solutions.
-
May 16, 2023 COMPOUND
INTEREST - most important math?
1329 4009
----------------------------------------------------------------------------------------
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--- to:
------
jamesdetrick@comcast.net
------ “Jim Detrick” -----------
--------------------- --- Wednesday, May 17, 2023
---------------------------------
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