# 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.**

**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