Exponential Growth

exponential-growth

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Exponential Growth

And How it Can Help You Retire Sooner

“The most powerful force in the universe is compound interest” -Albert Einstein

Exponential growth: Growth whose rate becomes ever more rapid in proportion to the growing total number or size.

A physical example:
■ A piece of paper:
● .1mm thick
● Fold it to see exponential growth:
○ 3 folds:
■ As wide as your fingernail
○ 7 folds:
■ As thick as a notebook
○ 10 folds:
■ The width of your hand
○ 17 folds:
■ Height of a 2 story house
○ 30 folds:
■ Through the earth’s atmosphere
○ 50 folds:
■ The distance from sun to earth
○ 60 folds
■ The size of the solar system
○ 100 folds
■ Radius of the known universe

It works with money too:
■ Double a penny every day for a month:
● Cumulative amount:
● Day 1: $.01
● Day 5: $.31
● Day 10: $10
● Day 15: $327
● Day 20: $10,485
● Day 25: $335,544
● Day 30: $10,737,418

We see exponential growth in tech:
■ Moore’ Law: Every 18 months the processing power you can squeeze onto a computer chip doubles
■ Kryders Law: The density of hard drives doubles every 13 months
● Cost of a gigabyte over time:
○ 1981: $300,000
○ 1987: $50,000
○ 1990: $10,000
○ 1994: $1,000
○ 1997: $100
○ 2000: $10
○ 2004: $1
○ 2010: $.10
○ 2014: $.026


How you can apply it to your money:
○ Compound Interest = Exponential Growth
○ The Rule of 72: In order to approximate the number of years it takes to double an investment, divide the growth rate into 72
■ Ex. if an amount is growing by 10% per period, it will take approximately 7.2 periods (73 divided by 10 = 7.2) to double.
○ The power of interest rate:
■ Years it would take until investment doubles:
● 1% interest: 72 years
● 2% interest: 36 years
● 4% interest: 18 years
● 6% interest: 12 years
● 8% interest: 9 years
● 10% interest: 7.2 years
○ US stocks historically compound annual return of 8%

■ Invest $2,000
● Year 1: $2,000
● Year 5: $2,938
● Year 10: $4,317
● Year 15: $6,344
● Year 20: $9,321
○ Without touching your money, you have earned $7,321

■ $2,000 Investment with regular contributions of $2,000 per year:
● Year 1: $4,320
● Year 5: $15,611
● Year 10: $35,609
● Year 15: $64, 933
● Year 20: $108,168
○ By investing $2,000 per year, you have earned $68,169

Compound interest is a powerful thing. Start investing now, enjoy later.

Exponential Growth

Sources:
http://raju.varghese.org/articles/powers2.html
http://www.oxforddictionaries.com/us/definition/american_english/exponential-growth
http://www.life123.com/parenting/education/math-activities/exponential-growth-facts.shtml
http://www.pcmag.com/encyclopedia/term/64169/kryder-s-law
http://www.geekosystem.com/gigabyte-cost-over-years/
http://www.theregister.co.uk/2014/03/25/google_price_slash/
http://arborinvestmentplanner.com/what-is-exponential-growth-double-time-and-the-rule-of-72/
http://www.heartlandfunds.com/individual-investors/Heartland-Funds-Account-Resources/The-Rule-of-72.htm
http://www.bankrate.com/calculators/savings/compound-savings-calculator-tool.aspx