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:
â A piece of paper:
â .1mm thick
â Fold it to see exponential growth:
â 3 folds:
â As wide as your fingernail
â 7 folds:
â As thick as a notebook
â 10 folds:
â The width of your hand
â 17 folds:
â Height of a 2 story house
â 30 folds:
â Through the earth's atmosphere
â 50 folds:
â The distance from sun to earth
â 60 folds
â The size of the solar system
â 100 folds
â Radius of the known universe
It works with money too:
â Double a penny every day for a month:
â Cumulative amount:
â Day 1: $.01
â Day 5: $.31
â Day 10: $10
â Day 15: $327
â Day 20: $10,485
â Day 25: $335,544
â Day 30: $10,737,418
We see exponential growth in tech:
â Moore' Law: Every 18 months the processing power you can squeeze onto a computer chip
doubles
â Kryders Law: The density of hard drives doubles every 13 months
â Cost of a gigabyte over time:
â 1981: $300,000
â 1987: $50,000
â 1990: $10,000
â 1994: $1,000
â 1997: $100
â 2000: $10
â 2004: $1
â 2010: $.10
â 2014: $.026
How you can apply it to your money:
â Compound Interest = Exponential Growth
â The Rule of 72: In order to approximate the number of years it takes to double an
investment, divide the growth rate into 72
â 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.
â The power of interest rate:
â Years it would take until investment doubles:
â 1% interest: 72 years
â 2% interest: 36 years
â 4% interest: 18 years
â 6% interest: 12 years
â 8% interest: 9 years
â 10% interest: 7.2 years
â US stocks historically compound annual return of 8%
â Invest $2,000
â Year 1: $2,000
â Year 5: $2,938
â Year 10: $4,317
â Year 15: $6,344
â Year 20: $9,321
â Without touching your money, you have earned $7,321
â $2,000 Investment with regular contributions of $2,000 per year:
â Year 1: $4,320
â Year 5: $15,611
â Year 10: $35,609
â Year 15: $64, 933
â Year 20: $108,168
â By investing $2,000 per year, you have earned $68,169
Compound interest is a powerful thing. Start investing now, enjoy later.
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