## 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