Monday 260615

 Mostly summarized from Gregory Mankiw’s Principles of Economics, 5th Ed.

PART 9 The Real Economy in the Long Run
Chapter 27 of 36 Basic Tools of Finance
Section 5 of 16
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Compounding and the Rule of 70
Country A has an average growth rate of 1% per year, and Country B has an average growth rate of 3%.
This two percent difference might seem insignificant.
Small yearly percent growth rates become large after compounded over many years.
Suppose Jerry and Elaine take their first jobs at the age of 22 and both earn $30,000 a year.
Jerry lives in an economy where GDP and incomes grow at 1% per year.
Elaine lives in one where GDP and incomes grow at 3% per year.
Forty years later both are 62 years old.
Jerry earns $45,000 yearly.
Elaine earns $98,000 yearly.
The difference of 2 percentage points in the growth rate has made Elaine's salary more than twice Jerry's.
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“The rule of 70,” helps to understand growth rates and the effects of compounding.
According to the rule of 70
· if some variable grows at a rate of X percent per year
· then that variable doubles in approximately 70/X years
In Jerry's economy incomes grow at 1 percent per year, X = 1.
So it takes about 70 years, 70/1, for incomes to double.
In Elaine's economy incomes grow at 3 percent per year, X = 3.
So it takes about 23 years, 70/3, for incomes to double.
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The rule of 70 also applies to a savings account.
In 1791 Ben Franklin died and he left $5000 to be invested for 200 years
to benefit medical students and scientific research.
If this $5000 had earned 7 percent per year the investment would have doubled in value every (70/7) 10 years.
Over 200 years it would have doubled every 10 years, 20 times.
At the end of 200 years of compounding the investment would have been worth about $3.8 billion
With interest rate of 1% at the end of 200 years the $5000 would have become $36.6 thousand.
With interest rate of 3% at the end of 200 years it would have become $1.8 million.
With interest rate of 5% at the end of 200 years it would have become $86.5 million.
Franklin's $5000 grew to $2 million over 200 years and would have been higher but for some of the money being taken out and spent.
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Growth rates and interest rates compounded over many years can result in huge gains.
An economy starting at $200 with high taxes and a 1% growth rate after 200 years rises to $1463.
An economy starting at $200 with low taxes and a 4% growth rate after 200 years rises to $509,778.
A saying often attributed to Albert Einstein is: "Compound interest is the eighth wonder of the world."
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medical students and scientific research
igaku-sei to kagaku kenkyū
医学生と科学研究
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How can the increasing of the U.S. GDP growth rate by one or more percent be best achieved? ChatGPT:
Most economists believe the best way to raise U.S. GDP growth by one percentage point or more is through a combination of policies that increase productivity and investment.
This can be done by measures including:
-maintaining a competitive tax and regulatory environment
-encouraging business formation and capital investment
-improving education and workforce skills
-investing in infrastructure and scientific research
-promoting innovation and the adoption of new technologies such as AI
-increasing labor-force participation and skilled immigration
-preserving stable fiscal and monetary conditions
Sustained faster growth would require progress on at least several of these fronts at the same time.