A Penny Doubled Everyday
July 10th, 2006 by Alan YuA few years back I was having a conversation with some people on how whenever you decide to invest in something for the long term, you should always think ahead on what would be the best choice in the long run while having persistence to follow through with it. The scenario was that if you were given a choice to receive one million dollars in one month or a penny doubled every day for 30 days, which one would you choose? When I first heard this, I knew that the penny doubled everyday must have been the better choice to go with as it was a little obvious to me that it had to be a trick question of some sort. But how much better would it be was not something that I knew immediately. So to demonstrate this, it was actually written out with all the calculations and it turned out to something like this:
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
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
Day 21: $10,485.76
Day 22: $20,971.52
Day 23: $41,943.04
Day 24: $83,386.08
Day 25: $167,772.16
Day 26: $335,544.32
Day 27: $671,088.64
Day 28: $1,342,177.28
Day 29: $2,684,354.56
Day 30: $5,368,709.12
Quite a big difference once you look at it as you would be getting over 5 million dollars with the penny doubled everyday for 30 days route. The funny thing when I look at this is how it is almost like starting a business and trying to make a profit. In the beginning you struggle a lot to get things going and afterwards once it reaches to a point it just takes off smoothly. How does that analogy go again……it is something like starting a business is like a rocket ship taking off into space. You spend 80% of your fuel during take off and once it reaches a certain point it flies smoothly with minimal consumption.
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March 3rd, 2007 at 8:11 pm
thank you for sharing that in the internet.
April 19th, 2007 at 4:05 pm
This was a wonderful lesson. I was thinking just like Mr. Alan Yu. I went with the penny doubled everyday. When I seen just this actually visualized. What a remarkable difference.
I enjoy reading lessons like these. You can become more insightful.
Thank you
Audre Chaney
April 20th, 2007 at 6:43 am
Well, if the question was “Would you rather have a million dollars, or a penny doubled every day for 27 days,” the lesson wouldn’t really be there, would it?
Don’t be afraid to challenge your assumption…because eventually, somebody else will.
May 9th, 2007 at 8:59 pm
actually joewatch the lesson would still be there. because the 5+ million dollars is just day 30. Now you have to add all 30 day together. so even at day 27 you should have in excess of 1 million dollars.
at the end of 30 days when you add the sum of all 30 days you have over 12 million dollars.
May 18th, 2007 at 5:25 am
On the “start with a penny and double every day for 30 days
= $ 10,737,418.24″
By my calculation (2) raised to the 29th power is
1,073,741,823.00 which a factor 100 times greater than your answer .
May 18th, 2007 at 10:11 pm
Wow, this is starting to feel like a math class for what was intended to be more of a expanding one’s way of thinking type of post.
But in general, $10,737,418.24 would be the 31st day if you were using the penny route. My guess is that your calculation was based on the fact that you first went .01 cent multiplied by 2 which equals .02 and you considered that as day one when really the first day should be just the one penny.
Similar to your next example, it seems like you went 2 multiplied by two which equals 4 and you considered that as day one when the first day should be the two by itself. Otherwise your 29 day calculation is really using thirty days for that example.
Just to note, the number I came up with in your example would be 1,073,741,824.00 with the way you calculated it and I’m not really sure what you are exactly implying with the 100 times greater statement as if you are multiplying it by “2″ you are basically trying to say “Two dollars doubled every day” which of course would be a lot greater in value. For 29 days to get similar results you would have to calculate it as “.02″ doubled for 29 days.
December 3rd, 2007 at 7:14 pm
The original information is correct, all comments are wrong. My dad needed this answer for a test in his job an there was NO answer over 5.5 million. BTW: His answer was right.
December 3rd, 2007 at 7:16 pm
well, not ALL comments are wrong:)
December 30th, 2007 at 11:35 am
What everyone has forgotten is if you start with a penny and the next day you double it at 2 pennies, well you actually have a total of 3 pennies…..so at the end of the 30 days make sure you add up all the numbers. This would be about double of what your final day number is.
January 9th, 2008 at 3:45 am
No the $ 5.4 million (approx.) should be the final result, as double your money means that yesterday’s sum is already included in today’s amount.
January 24th, 2008 at 5:21 pm
Ok, not to harp on about this, but if you use the power method, what exactly would you do to get the right answer?
would it be .02 raised to the 28th power? What is the equation for this?
January 29th, 2008 at 5:29 am
It is a simple question with a simple answer. Why do you make something out of it that it is not?
February 21st, 2008 at 6:07 pm
Just to let you know that on Day 24, you have entered $83,386.08, when in fact it should be $83,886.08, but the amount on Day 25 and all others are correct. Just a typo error when entering the amount.
February 21st, 2008 at 6:42 pm
Good eye there Deb. I’ve made the change. Thanks.
March 18th, 2008 at 6:19 pm
What is the darn equation for the love of god tell me!!!!!
March 24th, 2008 at 6:24 pm
So.
Any ideas on how to actually apply this?
It’s one thing to double one penny to two (”Oh, look. There’s a penny on the floor. I just made it to step two.”). But how on earth would you keep this up consistently for 30 days straight. That’s one month. One million in one Month?!
April 18th, 2008 at 7:31 am
Adjust your income for taxes and see how things work out
Take a penny and reduce it by 28% for income taxes then double the $.0072 and reduce it again before doubling and so forth.The TOTAL income net of taxes is only $922.04.
There is a real lesson here. There is real power in doubling your money but only if you shelter it from taxation.
Tim
There is a great lesson here
April 18th, 2008 at 8:18 pm
edward fernandez said 2 raised to the 29th power was 1,073,741,823. Strange. I use a scientific calculator available on the internet (http://www.calculator.com/calcs/calc_sci.html) and I get 536870912. If I raise 2 to the 30th power, I get
1073741824.
April 23rd, 2008 at 8:04 am
edward fernandez made a basic mistake, it is the correct number but he forgot it was pennies (.01) and not dollars (1.00), so you divide by 100. The correct total for the 30 days is $10737418.23.