## 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