The Magical Doubling Penny

Go pennies go!

Go pennies go!

Way back when Mr. 1500 was in high school, a teacher asked the following question:

“Which would you rather have, $10,000 or 1 cent that doubles in value every day for a month?”

I have no idea what I thought, but I do remember most kids saying they’d take the $10,000. However, if you do the math, the penny is the clear winner. It’s pretty neat to run the numbers:

Day 1:  .01
Day 2:  .02
Day 3:  .04
Day 4:  .08
Day 5:  .16
Day 6:  .32
Day 7:  .64
Day 8:  1.28
Day 9:  2.56
Day 10: 5.12

On the 10th day, we have a lowly $5. Whoop dee doo.

By day 20 though, things start to get interesting. Our little penny has now turned into $5000:

Day 11:  10.24
Day 12:  20.48
Day 13:  40.96
Day 14:  81.92
Day 15:  163.84
Day 16:  327.68
Day 17:  655.36
Day 18:  1,310.72
Day 19:  2,621.44
Day 20: 5,242.88

Days 21 to 30 are where things get nuts:

Day 21:  10,485.76
Day 22:  20,971.52
Day 23:  41,943.04
Day 24:  83,886.08
Day 25:  167,772.16
Day 26:  335,544.32
Day 27:  671,088.64
Day 28:  1,242,177.28
Day 29:  2,684,354.56
Day 30: 5,368,709.12 

Holy cow, see that last number? Had you chosen the penny option, you’d be a millionaire 5 times over. You better hide out from the folks who took the $10,000 option as they are going to be out for your money!

What is the point of all of this? There isn’t such a thing a penny that doubles every day. Well, maybe Enron stock, but you know how that one turned out. However, there are a couple very important lessons to learn from my teacher’s little example:

Space rabbits

Space rabbits

1) Compound interest is a powerful thing. Put some money away and it will make more money. Then, that new money starts making money. On and on and on, you get the picture. This happens in biology and even on Star Trek.

2) Giving your dollars enough time to reproduce is important. In the example above, after the first 20 days, we have a measly $5000. The last days are where the big magic happens. It takes big money to make bigger money and starting early gives those dollars enough time to multiply and work for you.

Let’s forget about the magic penny and look at a real world example. Of couse you can’t expect your money to double every day, but you won’t be starting with a penny either. Let’s say Dave starts when he’s 25 with $20,000 and decides never to add another penny. The stock market returns about 10% a year, which means your money will double about every 7 years:

  • Start at 25: $20,000
  • 32: $40,000
  • 39: $80,000
  • 46: $160,000
  • 53: $320,000
  • 60: $640,000
  • 67: $1,280,000

Wow, Dave’s little $20,000 has now turned him into a millionaire. Now, think about what Dave’s nest egg had he decided to continue to contribute beyond the original 20K!

The doubling penny, while an extreme example, has a lot to teach us about investing. Start saving when you’re young and you can spend your golden years on a beach instead of working as a Wal-Mart greeter.

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19 Responses to The Magical Doubling Penny

  1. Elizabeth says:

    I think the $20K at 10%/year is about as realistic as the doubling penny these days ;) But I think it’s important to remember to give money time to grow. I’m only several years into having a “real job” out of grad school, and it has been frustrating with the recession to not see my savings and investments grow.

    I wonder what my spreadsheets will look like 30 years from now, though!

    • 1500 says:

      Hi Elizabeth-

      Yeah, you just had the misfortune of entering the workforce at a bad time. Misfortune may be too strong of a word though. The economy seems to be on a gradual upswing now. If you’ve been saving diligently all this time, you’ll be rewarded when the economy really turns the corner. Think of it as buying at a discount.

      Also, think of how you would have felt if you got a job in late 90s? The crash of 2000 wiped out a lot of wealth.

      In any case, its best to ignore the market fluctuations. Slow and steady wins the race.

      In 30 years, I’ll bet you’ll be very happy that you made wise decisions now!

      • Two Percenter says:

        The lesson here isn’t to save your way into wealth. It is the power of duplication. Using money to make money is one way, investing and risking hard-earned capital to try to make more, but it isn’t realistic to expect 10% growth in any investment vehicle in today’s economy.

        Take advantage of US’s free enterprise system and go into business for yourself and duplicate yourself that way. 98% of the population focuses on how to save money to invest the saved money.

        Only 2% focuses on how to EARN more money. Big difference.

        And no, it doesn’t take money to make money. Ever seen a baby born with a handful of cash?

        • 1500 says:

          “Take advantage of US’s free enterprise system and go into business for yourself and duplicate yourself that way. 98% of the population focuses on how to save money to invest the saved money.”

          Interesting point and I like the way you think. The US education system seems to teach us all how to be indians and not chiefs. We grow being taught that we can be a firefighter or pilot or banker. I don’t ever remember being taught about entrepreneurship.

          I’m trying to instill these traits in my daughters though. THe 7 year old will be starting a bird house business later this year.

    • Kurt says:

      Well 2013 was a 30% gain in the market… so it may be realistic after all. ;)

      Hope you were buying when you wrote this!

  2. This is not an unfortunate time! The first rule of investing is buy low, sell high. If you have investments in your portfolio that you believe are worth more than they are currently trading, and that as the economy improves the market will start to realize that worth, then you are going to be poised to see some good yields. I hear professional investors all the time that if they like an investment when the price is $10, they like it even more if it is trading at $5. It just means they can buy more of it, averaging down their cost, so that when the market corrects itself they can enjoy a larger gain.

    And also think of it this way: You have now seen what the economy can do. This is a lesson that hopefully you will keep with you always so that you appropriately manage risk going forward. Great learning opportunity!

    • 1500 says:

      Lacy-

      Very well put! The economic crisis of 2008 was a perfect example. Plenty of good companies got dragged down for external reasons making for a perfect buy opportunity.

      I also think of Warren Buffett. There were 2 times in his investing career where he sat on the sidelines for years because he knew the markets were overbought. As soon as they came back to normal, he threw billions back in.

  3. Brian says:

    I remember getting this same question when I was in school. I have no idea what I picked (if I had to guess I probably picked $10K since it seemed so large at a young age). It is a great example to show how important it is to start saving as soon as you can so you can get the maximum return.

    • 1500 says:

      Yeah, I give this example to college graduates all the time. Unfortunately, I don’t think most people learn or appreciate the lesson until up in their years.

  4. I am waiting for the interest magic to happen. My measly savings need to grow exponentially in the next 12 years so I can retire.

    Tribbles not space rabbits. I am not a financial expert but I am a Star Trek expert.

    • 1500 says:

      Jane, sit tight. We’re coming out of economic doldrums. I think we have some good times to look forward too.

      Yeah, “Trouble with Tribbles” is a classic. I remember watching this as a young child. Its probably what turned me on to Star Trek.

  5. Funny you should write about this. For some reason this exact memory popped into my head a few days ago. I tried going through the math in my head and stopped around the mid-teens because it wasn’t even close once you look at the numbers.

    • 1500 says:

      JC-

      Small world!

      I like the focus of your blog. Dividend income is becoming more important to me as I look to get out of growth stocks and into investments that generate income.

      While not entirely passive, have you taken a look at becoming a lender on Prosper or Lending Club? I’ve been doing it now for almost 3 years and thinks its great.

      • I would be using it for a small portion of my portfolio, but unless the laws have changed recently my state doesn’t allow it. So I’d be stuck with only using the secondary market. I’ve heard that there’s still money to be made there, but to me it seems like more of a headache to try and find high quality loans that won’t default from the secondary.

        • 1500 says:

          Agreed. I don’t bother with the secondary market.

          I think Lending Club is supposed to be available in all states this year, so keep an eye on it.

  6. Pingback: The Most Valuable Day of my Life | 1500 Days to Freedom1500 Days to Freedom

  7. Awesome post 1500! Fellow financial freedom blogger here. I must admit it’s such a profound yet simple idea that a penny doubled can turn into millions more than a one time lump sum. A penny is a metaphor everyone can relate to and I think it speaks to the underlying truth of short term gratification vs. Long term gratification. Do you have any other stories like this?!

    -Davey Pockets

    • 1500 says:

      Thanks Davey Pockets! Yeah, it is an amazingly powerful example. Of course money doesn’t double daily, but we’re also starting out with much more than a penny.

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