What is Compound Interest? With examples.

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What if you had two options: A, I give you $1,000,000.00 today or B, $0.01 today, but every month, I’ll double the amount I give you, for the rest of your life? Which do you choose?

If you’re smart, you’d choose option B because by the compound interest equation:

A=P(1+(r/n))^(n*t)

where:

  • P is the initial principal balance
  • r is the interest rate
  • n is the number of months in a year that the interest is being compounded
  • t is the number of years elapsed
  • A is the future value

You know that by year 30, you’ve become a billionaire. How?

You know, since P = 0.01, r = 1 (100% interest), and n = 12 (12 months per year). Then by year 10, where t = 10, your new balance is $148.41. Then, two years later, by year 12, when t = 12, your balance gains a 0, to $1,013.31. Finally, by year 20, your balance breaks $1M, to $2,202,447.18 = $2.2M. You win!

Even if you chose option A, $1M, and invested it in the stock market, averaging a 10% return annually, over the same timeframe, governed by the same equation – you’d have $7.33M by year 20. Not bad for the average investor. To the uninitiated, choosing the penny still seems to be a terrible idea, observe graph 1.

Graph 1: Compounding Choices Over Years 0-20.

Except, now, we’re comparing investment returns, and by year 25, what happens? $0.01 compounds to $268M where the $1M compounds to $12.06M. Year 30? $0.01 compounds to $32.7*10^9, or $32.7B, while the $1M compounds to $19.8M, observe graph 2.

Graph 2: Compounding Choices Over Year 0-30

Assuming you’re a young 20-year-old, by 50 years old, you’d be a billionaire, while your uninitiated counterpart, who chose the $1M out of ignorance, is left in the dust.

Behold! The eighth wonder of the world – compound interest.

This Post Has 2 Comments

  1. Lakandra Louding

    I’m not sure if you’re a physicist or just an amazing mathematician but I just saw your page on Instagram and ended up here. I wish more people knew about you

    1. Gil

      I appreciate your kind words. I am a student of physics, great guess!

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