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-------------------- 2482 - MATH - interest rates and growth
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- This really is the most important math you will ever learn. It not only affects you personally it tells you how to understand the world:
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- 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.
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- The formula is simple. It is : Interest rate * years = 70
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--------------------------------------- i * t = 70
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- 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?
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---------------------------------- 70 / 10 years = 7% per year.
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- 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?
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- 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:
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----------------------- 70 = 100 log to base “e” of 2
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---------------------- 70 = 100 ln 2
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----------------------- ln 2 = 0.693147
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- 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.
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- 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.
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------------------- 70 / 2% = 35 years.
- In 35 years, in the year 2046 the population will be 14 billion unless we lower the growth rate.
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- 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.
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--------------------------------------------------- Pennies ------ Pennies
-------------------------------------------------- Contribution --- Total
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-------------- 0 ------------- December 1 --------- 1 ------------ 1
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-------------- 1 ------------- December 1 --------- 2 ------------- 3
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-------------- 2 ------------- December 1 --------- 4 ------------- 7
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-------------- 3 ------------- December 1 --------- 8 ------------- 15
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-------------- 4 ------------- December 1 --------- 16 ------------ 31
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-------------- x ------------- December x +1 ----- 2^x ----- 2^(x+1) -1
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-------------- 23 ------------- December 24 ------ 2^23 ---------- 2^24 -1
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-------------- 23 ------------- December 24 ------ $83,886 ----- $117,772
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- You can see that doubling every day is the same as 2 raised to the number of days. The first day is zero.
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- 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.
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- 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.
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- 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.
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- 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!!!
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- 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.
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- The chief cause of problems is solutions.
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- November 12, 2019 2482 1329
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--------------------- Tuesday, November 12, 2019 --------------------
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