A 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 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: $83,886.08
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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thank you for sharing that in the internet.
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
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. 🙂
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.
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 .
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.
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.
well, not ALL comments are wrong:)
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.
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.
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?
It is a simple question with a simple answer. Why do you make something out of it that it is not?
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.
Good eye there Deb. I’ve made the change. Thanks.
What is the darn equation for the love of god tell me!!!!!
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?!
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
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.
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 $10737418.23.
❓ Actually, you are all wrong when considered what he said. See he is inacurate to what he saying. Because if you get one penny a day and double it, its only .02 cents per day.. not compounded daily. See if the question was to be worded, if you doubled the amount in your bank starting with a penny, then it would be a large number. The quote “a Penny doubled everyday” is not right. that would really mean, day 1 = .01 * 2 = .02.. well now on day 2 + .01 *2 = .02. Now you have .04 cents in the bank after 2 days. …and so on.. so you really aren’t saying the right words.
The scenario = “if you were given a choice to receive one million dollars in one month or a penny doubled every day for 30 days, which one would you choose?” The way this scenario is worded means that you will only receive 2 pennies every day for 30 days. ONE penny doubled (0.1×0.2) will ALWAYS equal .02! Reword the scenario and the title of this thread because it doesn’t make sense to choose a penny doubled every day over 1 million dollars.
😯 ZOMG what’s the frickin mathematical formula to figure it out?!? 😯
you guys are so arguementative. “he is right, you are wrong!”. just get over it, their just numbers. 😡
Okay…I just saw this on the happening. And I wasn’t sure about it, because the guy said that you would have over 10 000000$. So day 1 is 0.01$ and day 2 is 0.02$ and day 3 is 0.04$ and so on, but after day 30, do you add every day together? or just end with $5,368,709.12?
Anyone have a straight answer to this one 😯
Zoggy, You would have to add all the days together, per on day one you have .01 and day two you get .02 handed to you, So really on day two you would have a total of .03. So if you add everyday together, per your doubeling the previous days amount.
Bottom line, doubling with a penny ads up quick IF you can stomach dropping 500k to TRY to double it with stocks. Start a mock portfolio with think or swim and put it to the test. 🙂
WOW, most of you are way too technical. It’s an analogy people. An example on how compounded efforts (and interest) work. For success to occur you need to give the most on the front end for a large of amount of time, but even though you may not see immediate results they are compounding and the pay off will occur if you have the tenacity and intestinal fortitude to stick with it. whatever “IT” may be.
By adding in the choice of the million in one month, it shows the danger of always going for the quick and easy. It may work out OK but you may be missing out on a much bigger and better deal.
CARA, To get any particular dayâ€™s amount use this formula: 2 raised to the (n1) power . To help you understand, on day 1 (n=1), the total for that day is 2 raised to the (11) power = 2 raised to the (0) power = 1. In fact, on day one you receive one cent. Likewise, on day 5 (n=5), the formula gives â€œ2 raised to the 4th power (51)â€, or sixteen cents.
To get the sum of all thirty days, use:(([SIGMA]2 raised to the (n1) power)), n from 1 through 30
(this means you calculate the formula for the first day and then again for each succeeding day and you keep adding the totals every day), from 1 to 30. To get the sum up through any other number of days, just use that number of days for â€œnâ€. After youâ€™ve tried this out a few times, here is a shortcut (actually this is the solution for the summation formula I gave above – the second formula with the Greek â€œsigmaâ€).
The sum through â€œnâ€ days is 2 raised to the (n)power less 1. So, on day 5 you have â€œ2 raised to the 5th power less 1â€, which is thirtyone cents, and that, indeed, is equal to the 1 cent, plus 2 cents, plus 4 cents, plus 8 cents, plus 16 cents (5th day), that youâ€™ll get doing it the summation way (but now you understand).
Sorry, but this editor won’t allow me to paste the mathematical symbols/formulae (which would make this easier to read).
Thank you. Me and my dad were dicussing this and he didnt believe me. So than k you for doing this!!!!!!!!!!!!!
This was a GREAT blog! I’m at work right now contemplating actually doing this project…if only I can just get to day 28! 😛
julian is correct, you have to now add all the numbers together, you get a penny on day one, two pennies on day two, 4 pennies on day three, at the end of 3 days you have 7 pennis, not four.
I knew this for years, the right answer is
$5,368,709.12 for 30 days.. 31 Days > 10,737,418.24
Thats What it is!
If you get to keep your 1 cent the first day, two cents the second day, etc., you will have a total of $10,737,418.23 at the end of 30 days. THAT’S the correct answer. You don’t lose every single day’s investment and have it replaced by twice the amount. It adds up every day, like interest in the bank adds up.
[2^(n1)]/100
Here is the REAL DEAL answer to everyones questions!!
If you start with 1 penny(your principle) on day one and double it each day for thirty days (meaning that you are earning intrest then at the end of 30 days you will have 536,870,912 pennies which will be $5,368,709.12.
However, there is another scenario that says someone will pay you 1 penny on day 1 and double the amount they pay you on each additional day there after for 30 day. this means they pay you (1 penn on day 1) (2 pennies on day 2) (4 pennies on day 3) (8 pennies on day 4) and so on….. since they are paying you at the end of each day you keep the money from each day.
Therfore you will add up the total for days 1 through 30. this means they will have payed you
1,073,741,823 pennies or $10,737,418.23
The actual formula is (2^n)1 for your answer in pennies, divided by 100 for the answer in dollars.
EG: (2^3)1=7
1+2+4=7.
Real answer is 10,737,418.23 for a thirty day month.
This was hilarious! So many people needing to prove their answer was the right answer just got better and better as I read each entry. I was totally cracking up. Then, the tax issue. That just blew me away!
Thank you all for making a boring day bearable.
I’m the dumb one here. But all my life I’ve loved gigantic numbers!!!!!!!!!!!!! Any way I was wondering what would be an easier way to figure the amount after 2 months 3 months etc.
😈 😈 10 million doller’s! i’m going to get a legal document and see if anyone would sighn to give me a penny a day and double it in return for 1 million
Steigertiger you are the dumb one because the formula is listed ABOVE!!!!! Just put in the numbers and pooof the answer appears…Now if you cannot figure this out call hooked on phonics for numbers. 😯
The calculation on day 24 is wrong, I believe it would be 83,886.08.
a 31 day month would be $24,159,320.76 😆 ❗
that is the actual sum of all the days. =]
2 to the power of 30=1073741824 or 1073741824 pennies. 100 pennies make a dollar. 1073741824 divided by 100=$10,737,418.24. I don’t think I’m wrong but if I am o well.
No No Josh A, if that is your name,and we all know its propable not. A 31 day month would be $21,474,836.47 however I’m sure you have realized your mistake. By the way Gubble Bum you my friend are correct;)
i think everyone is to analytical on the wording of the secerio its meant for fun. however for the people that are confused about whether you have 5 mill or 10 mill what is happening is that the amount of money you are given is doubled meaning that if you have 4 cents you are not given 8 cents the next day you are given 4 cents they are matching the money in a sense doubleing it everyday so on day 30 you have roughly 5 million dollars and on day 31 you will have 10 mill not 10 million on day 30 just cause you can add the numbers please take an accounting class to learn more
It’s a great way to increase money, but interest doesn’t double your money. It’s only a fraction percentage of th eprincipal, which means you actually have to deposit the dobled amount. I don’t know about you, but I don’t have $167,000 to deposit on day 25 to double it!
Just my 2 cents worth (get it? 2 cents!)
shoot, i dont have the money i need to put in on day 12. what are you talking about?
but i sure would love to do this and get rich if i had it to do. lol.
shay.
Ok… I teach high school math and a student posed this problem to me. I gave her an answer and she didn’t believe me, so we came across this in trying to verify. Here’s how I explained it to her…
Day 1 = 0.01 = 2^0(.01)
Day 2 = 2(0.01) = 2^1(.01)
Day 3 = 2(2(0.01)) = 2^2(.01)
Day 4 = 2(2(2(0.01))) = 2^3(.01)
and so on…
Day 30 = 2^29(.01) = 5368709.12
Okay I’m getting the same answer as most of you which is the total for 1 month is 10,737,418.23. I had to do this in my college math class. We were supposed to figure out that and then figure out how many DAYS it would take to become a googolaire….10 to the 100th power. Anyone know the answer to that???
The answer is on a 30day month, you would end up with $5,368,709.12. In a 31day month, you would end up wih $10,737,418.24. You have 1 penny on day one, 2 pennies on day 2, 4 pennies on day three, and just keep doubling what you had the prior day for the next day. That is how you get this result.
That is just saying how much you get paid each day. It’s not saying how much you made for the entire month.
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: $83,886.08
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
Add it all together and you get 10737418.23
thanks needed 2 figure it out 4 extra credit in class
🙂
🙄
suckers its all wrong he didnt carry over any thing i am always right
😈
when do u check this stuff peeps rite ❓
I’d keep only one penny! (one from 1966). you can keep your million!
hahaha i asked this girl in my class if she would rather have a quarter a day for a month or a penny doubled everyday and she said “is that a trick question, a quater a day duhh!” 🙄 then i told her that with a penny doubled you get more than a million dollars and she wanted proof so thank you for all the proof i need! 😮
Every day, you only add enough pennies to double the amount. You don’t add twice the amount every day. Start with a penny.
+1=2
+2=4
+4=8
+8=16
+16=32
+32=64
+64=128
+128=256
…and so on and so on. Every day, you match the previous day’s new sum. You don’t double it and then add the new amount. (Well, you could, if you have just that many pennies and wanted to really speed up the process). 🙂 But at the end of 30 days, you’d have $5,368,709.12. 😯
If you were really ambitious and were to actually double the amount and THEN add the pennies, you’d end up with about $10,737,418.23.
Trust me….if I had the pennies to do this every day, I wouldn’t be working my 85 job. 🙂
Guys! Gals! who cares if it gives 1 million, or 5 million, or 10 million, The point is, that it’s whatever million dollars richer than day 1!
impressive question. i’ve seen this on The Happening and my dilemma is: the final answer is with or without adding all days together?
and the amazing thing is that the amount earned in the 31st day is the same with the amount earned if 30 days are added together…
…i mean duh…they were doubled
i dont know its really addicting 😛
If you are strictly doubling the money and the final answer is 5,368,709.12 the the equation is
(x)*2^t
x being the amount started with on day 1
t being the number of days
if the answer is all of the numbers added together at the end, then the equation is
((.01)*2^29)*2
there are other pactical applications fo this equation
I do genealogy and have used this in figuring out the number of names that would be in a pedagree chart. In 45 generations there would be over 98 billion names.
I been working on this for years in my life and it work for me.double a penny in 2 years not 31 days.and I know how it work!
Don’t put on the powers it’ll give you the wrong answer if you actually try the doubling instead of finding a short cut you’ll get the right answer believe me I tried it. The final amount is $5,368,709.12. You don’t add the sums from all the days either
I’D HAVE TO SAY I’D TAKE THE MILLION DOLLARS. Because there is no such thing as a “penny” in my country. It is a CENT. Since there are no “pennies”, it would make One Million Dollars a much more profitable venture! 😀
Sorry Steven but you are wrong. It does work using powers. It is called math and there is an equation for everything. You just have to know how to use it.
It is funny how everyone loses the point of teaching something like this. The point is sometimes we settle for less than the best by conceding in life. If we keep working our outcome will be better than settling on a less than perfect surething. The last few days will in fact be our most productive if efforts are allout until the end!
another equation that could be used is the future value of a dollar equation. which is FV=PV(1+i)to the power of n
fv=0.01(1+1)to the 30th power
fv=.01 x 2 power 30
fv = 10,737,418.23
n= to the period which is 30 days ans i= interest factor which is 100% because it is getting doubled
so there u go another way
How do you figure this out using log on the calculator?
I know how to apply the scenario but it wouldn’t be in 30 days but even a year would be fine. Wouldn’t it?
Brian
sme people are saying that it wouls only be 0.02 cents every day because of the way its worded. while i fully understand how you got it isnt fully correct “a penny doubled every day for a month” is to have a penny double it, double it, double it, and so on as in the article.
it is a trick question they are supposed to trick you so you have been tricked, big deal who cares. it was meerly an article to get people to think in the long run.
What would be the formula to use if i was to design a program using a psuedocode? and the total has to be displayed in dollars.
“A PENNY EARNED IS A PENNY SAVED.”
A. LINCOLN SO START SAVING NOT DOUBLING.
…a penny saved is a penny earned…so start saving not doubling. here’s a very simple solution to that penny thing: 30 days=30 houses; on the 1st day you collected the 1st penny from the 1st house; 2nd day you collected 2 pennies from the 2nd house, and so on…at the end of 30 days, you have collected a total of 536,870,912 pennies which is = to $5,368,709.12. it means, there are no more pennies left among those 29 houses. thus, $10,737,418.24 in 30 days is not possible. 31 days, yes.
one time i deposited a gallon of pennies in the bank. do you know how much? just about $30hahaha. when usps started accepting pennies in vending machines, i used plenty of them to buy stamps.
or maybe you can use a bar graph. don’t worry about that penny thing. someday soon the govt. will phase out that coin.
I might only be 14 but i can tell you one thing dont matter what you get money you probly didnt have before so be thankful they put this site on for us!!
:):):):):):):):):):):):):)
😀 💡 just to let you know you guys are all really smart and if i were you i would try to get a good job and show people what you can do!
💡 🙄 😯
i JUSZ Wanted to leave a comment
OK now, I’ll settle this as this was looked at in many angles..First of all, I’m a retired math ‘guru’, if you will’ and it boggles my mind that some of the younger people on this subject were right and the so called math teacher was absolutely dead ‘WRONG’. Congrats to all you smart ones for looking at this with open minds and for the block heads out there here ARE the REAL FACTS: Sorry to…Stephen,DCecil21,certified ilokano american, Christene, and Shanna the math teacher…you are all wrong, you don’t need a 31st day to get the totel. You ABSOLUTELY DO need to add all the days because what you faled to realize is the fact that you KEEP ALL the pennys you recieve on EACH day. Look at the key words here and there’s a point in there. Gubble Bum, Mitchelllicous, Alisha, 2muchtime, and Josh are ALL CORRECT!!!!!! Pay GOOD attention to questions before you decide to give a dumb answer..(example) Every day you add the ‘doubled’ amount to ‘each’ total you got ‘each’ day so the total IS TRUELY>>> $10,737,418.23. THIS IS IT!!! NO IF’S AND’S OR BUT’S….
EXAMPLE # 2: You add day one total to day two total then you add both totals from day 1 and day 2 to day three then you add all three days to day 4 total and so on. If you still don’t get it, get help soon you poor souls,this isn’t that hard. ( the key word here is (DOUBLE) SO ‘YES’ the final number of 5,368,719.12 is ‘doubled’ because ALL the totals get added to give you $10,737,418.23 IS in only 30days NOT 31!!!!!!!
EXAMPLE #3…If this last example doesn’t prove the fact then the few of you who think you’re right REALLY need help…. On day one you get .01 on day ten you get 5.12 for ‘that day only’ on day 20 you get 5242.88 for ‘that day only’ on day 30 the amount of 5,368,709.12 is the amount you got for THAT DAY ONLY so THINK REAL HARD, what happened to the 2,684,354.56 you got the day before??? You STILL have what you got the day before and every day before that so this shows that you DO add EVERY SINGLE DAY TO EACHOTHER to give you $10,737,418.23 in 30 days. (THE END)
By the way, under a certain law wich was imposed a few years back that deals with anything we see on tv or movies or hear on radio certain facts MUST be mentioned CORRECTLY in nonscience fiction movies. Tha reason I mention this is because in the movie “The Happenning” actor John Leguizamo brought up this ‘penny doubled’ thing and HE gave the correct answer. This is only imposed to anything considerd educational info in movies since so many people are influenced by what they see in movies and though this movie is not a true story, the basic idea is (‘what if’) this movie teaches to think “what if”………………..
OK I had to come back on this cuz i read every comment and saw a lot of confusion on wording so I will once again settle this since I actually have the CORRECT wording in my hands as we speak:::: “If I gave you 1 penny today, 2 pennies tomorrow, 4 pennies the next day and keep doubling each days total every day after, how much will you have after 30 days?” The ONLY TRUE ANSWER IS $10,737,418.23 AS YOU WOULD “ADD” EACH AND EVERY DAY’S TOTAL TO EACHOTHER and that’s that.
Ok I’d like to comment on something that is causing
the comotion. It’s looking at the problem
from 2 scenarios. Some people are trying to multiply
by 2 and some are squaring when they should be
multiplying that days number times
itself for the next days amount.
Proof: Ok say John hits lottery and gives Lori $100
dollars ond Monday(Day 1). She’s so excited, but John
isn’t through yet. He tells her if she doesn’t spend and of $100
bucks, and she puts it in an envelope, the next day(DAY 2) he will
DOUBLE what is in envelope. looks inside, crisp $100 bill. Now it’s simple.
To double it, he must place ANOTHER $100 inside.
To her surprise, he continues on third day. Inside envelope
Lays Lauras $200. Think of double or nothing bet. Now he will place
$400 bucks inside.
Day 1 : $100 1 cent
Day 2 : $200 2 cents
Day 3 : $400 4 cents
Day 4 : $800 8 cents
Day 5 : $16,000 1,600 cents
Now this seems simple. BUT, depending on how you
take the question is the key: BOTH WAYS ARE RIGHT
Day 1 : $100
Day 2 : $200
Day 3 : $400
Day 4 : $1,600
Day 5 : $2,560,000
so if John doubles previous amount following Day 30, then
over 10 mill….
Day 1 = $0.01 (Now in total you have $0.01)
Day 2 = $0.02 (Now in total you have $0.03)
Day 3 = $0.04 (Now in total you have $0.07)
Day 4 = $0.08 (Now in total you have $0.15)
Day 5 = $0.16 (Now in total you have $0.31)
Day 6 = $0.32 (Now in total you have $0.63)
Day 7 = $0.64 (Now in total you have $1.27)
Day 8 = $1.28 (Now in total you have $2.55)
Day 9 = $2.56 (Now in total you have $5.11)
Day 10 = $5.12 (Now in total you have $10.23)
Day 11 = $10.24 (Now in total you have $20.47)
Day 12 = $20.48 (Now in total you have $40.95)
Day 13 = $40.96 (Now in total you have $81.91)
Day 14 = $81.92 (Now in total you have $163.83)
Day 15 = $163.84 (Now in total you have $327.67)
Day 16 = $327.68 (Now in total you have $655.35)
Day 17 = $655.36 (Now in total you have $1310.71)
Day 18 = $1310.72 (Now in total you have $2621.43)
Day 19 = $2621.44 (Now in total you have $5242.87)
Day 20 = $5242.88 (Now in total you have $10,485.75)
Day 21 = $10485.76 (Now in total you have $20,971.51)
Day 22 = $20971.52 (Now in total you have $41,943.03)
Day 23 = $41943.04 (Now in total you have $83,886.07)
Day 24 = $83886.08 (Now in total you have $167,772.15)
Day 25 = $167772.16
(Now in total you have $335,544.32)
Day 26 = $335544.32
(Now in total you have $671,088.63)
Day 27 = $671088.64
(Now in total you have $1,342,177.27)
Day 28 = $1342177.28
(Now in total you have $2,684,354.55)
Day 29 = $2684354.56
(Now in total you have $5,368,709.11)
Day 30 = $5368709.12
(Now in total you have $10,737418.23)
If your answer is 100 times greater than $10,737,418.23 you have to remember you started in pennies. There are 100 pence in every dollar. So the answer is $10,737,418.23.
End of Question.
What If It’s A 31 Day Month 😀
Thats it! I’m calling the FTC. Your all out of order, this whole thread is out of order!
I’m ending this right now…..
This has nothing to do with math. As others have eluded too. It is an issues of semantics…nothing more, nothing less. It is evident from the posts…that most of us can do the math…be it long hand or with a sci calculator, or if your a self proclaimed genius like myself…then you are fortunate enough to just run the numbers in your head and whala!
So really, it never should have been a discussion about math…but rather–a discussion about semantics.
Wait a minute! It should not have been a discussion about either of those things. What the hell was the point of the original post anyway?
See! Thats why I’m calling the FTC…there is trickery going on here, and I’m going to get to the bottom of it.
Incidentally, my interpretation of the post would have been the same as the authors. But I refuse to even mention a number…after having witnessed the blasphemous rantings of the masses.
So, in conclusion: Most of you neophytes meandered down the wrong path.
I can just feel the love already.
😛 The formula is (2^n2^0)/100.
Now let me tell you why this is wrong. Im going by your answers. You said by the end of the 30 days the pennies total 10,737,418.23 right? now what you are forgetting is this is the total amount in pennies. so 100 pennies equal $1.00 right? so you divide 10,737,418.23 by 100 and you only get $107,374.18 in dollars. This number is far from millions. So which make this NOT TRUE.
Moe is absolutely right. I was wondering when the smartest person in the world was going to appear,but there is one exception it’s not that total on the 30th day that’s the total for day 31( 10,737,418.23)
This was on the movie The happening, I didn’t understand the joke the guy told before the car crashed so I had to search it up on the internet, thankyou.
Just tossing it out there, you don’t add them all together. It states that the amount is double each day. This means on day 1 you have one penny, and on day two :::you only receive one penny, this would make 1+1=2 (doubled) therefore you don’t have three pennies after day two, you only have two. ect…
thx dude i needed this for my math hw
Now someone tell me this…If you start with a penny and double it everyday for 1 year, how much will you have then?
this is the (retardedest 😛 )thing i have ever read
a penny doubled everyday for 30 days is only sixty cents on day 30 !!!!!!!!!!
day 1= .02
day 2= .02 and soon until day 30 and he didn’t compound the totals of each day.It’s only two cents per day people.
yo. calculate deez nutz. 😆
Gotta love people who don’t understand exponential growth.
Here’s a quick, effortless way to figure this out.
1. Open Microsoft calculator.
2. Hit 1 * 2 =
3. Keep hitting = as many times as you’d like.
4. Experience exponential growth.
Also, doing this with pennies and a calendar is dumb. This question was originally asked with grains of wheat/rice placed on a chess board (over the total of 64 squares you’d have 18,446,744,073,709,551,615 grains of wheat/rice).
Your all idiots, get a life
Except for those of you who just looked this up for math homework. That was smart.
Wow, ummmn… this whole thread was unexpectedly funny.
Many are right in one way and wrong in another depending on interpretation. A simple concept of compound interest is approaching the complexity of a theological debate with multiple beliefs being related with each more adamant than the last about it’s own validity. Pretty soon this is going to have to be moved to a comparative religions thread in order for the discussion to fit the topic.
Several people have proving adequate math skills, it seems more the interpretation of the original premise that seems to be in question. As far as that goes … outside of a classroom it no longer matters what is said or meant once a thing is uttered. It only matters what a person hears or understands it to mean.
So to all of you with the adequate math skills… you are all right within the constructs of your own paradigm. 🙂
that’s my 2 bits as I couldn’t help but comment myself for some reason.
Wording is wrong. A penny doubled for 30 days. well isn’t that just 2 pennies everyday for 30 days? or 60 cents?
This was on an episode of walker texas ranger. and walker played by chuck norris gave the answer $5,368,709.12 so that has to be right because what Chuck Norris says goes! end of story.
nerds 😯
thanks haha alot of your answers are different by a penny soo i took the majority
“vote” and decided to us $10,737,418.23 ! woop EXTRA CREDIT ferr mee !
This is a wonderful tool to help people understand the POWER of Compound Interest. You don’t add a penny every day you DOUBLE your money every day.
Same thing with investing, you INVEST and have a goal of about 15% growth every year allowing you to DOUBLE your money about EVERY 5 YEARS. Your goal is to be a millionaire before you retire as that is what you will need to have to retire and live at the same level you are at NOW!
So if you need a million or MORE at retirement, break it down in reverse. I need a million dollars at age 67 when I retire with full social security benefits (if they are still available).
So taking age 67 as our ending point:
67 1 million
62 1/2 million
57 1/4 million
52 $125,000
47 $62,500
42 $31,250
37 $15,625
32 $7812.50
27 $3906.25
22 $1953.13
That works out to a weekly average of investing $37.56 per week, starting at the of age 22.
If you make $$375.60 per week after taxes you only need to save 10% of your income to be a millionaire when you retire.
If you make $751.20 every week after taxes and save 10% you will retire with $2 million, investing $75.12 weekly.
You’re all wrong—–for overanalyzing this. 😉 Whether it’s $5 million or $10 million, WHO CARES. I would take either ot hte $1 million cash for that matter.
After you get all of the answers after you add them all up you get 8,152,416.35 what about 31 days cause some months have 31 the what you get?
Now this is just the doubling figure. Most of us find more than 1 penny a day usually. Now while the calculation is correct that last calculation is what we’d get ON the 30th day. Now, you have to add up what you have made the entire thirty days which I believes adds up to somewhere around 42 mil. Now also add in the amount of pennies you got/found each day, that’s even more! I’m not going to take time to figure that out right now, but I will at some point.
I use nickels and triple them every day.
it aint none of ya bisness what da answer is and yes i know i spelled dat world wrong
What’s it matter about equation. Change it from 30 days to 30 Steps. I challenge all the equation freaks to actually applying this, and the first one to actually get to double there 1 on every step. Can be the formula winner in my books. Just share how, I think allot of people will appreciate this.
If you are to get that much a day, then you would recieve $1,073,741,823 on the 30th day. Yep! 1 billion dollars…hmmm should have I taken the 1 million? 🙂
Clearly, original doubling thesis never mentioned whether this was an investment notion or savings notion. Are you doubling your investment every day or are you adding up the doubling every day? Some people are assuming that on second day you will have total of 5 pennies. While some are assuming that on second day you will have total of 4 pennies. If the pennies are just multiplying on another plane and then adding up together, ya, add them all up. But if this is an investment notion where you put up 1 penny and it returns 100%, then you get 1 penny plus your earnings of 1 penny thus having a total of 2 pennies. This is more of your personality and greed test than anything else. There is nothing theoretical or metaphysical about this lame argument. People with investment experience will always see a total of 2 pennies on second day.
the equation you are looking for .01*2^30=10737418.24, I do not know what all that other mess was about, but there you are.
How much would them there pennies weigh? What is the metal in them worth? Is it permissible to convert the pennies into paper money for convenience sake? Do we have to report this to the IRS? If so, as earnings, a gift, investment, unexpected cash flow or imagination?
Did I miss the point of this post?
Wow! Sorry. Glad none of the rest did. I love you all.
Pee Ess
Uhhhh – – fergot whut I wuz aboot to say.
Guys, what if, just what if, a big group of people got together and managed this ‘penny a day’ thing in a way that it wouldn’t be too expensive for any one person, but all at the same time, at the end of the 30 days there would be a total of a million plus dollars to divide up amongst the investors. You know they all would get even more at the end because if they put all that money in the bank, they would also get the banks interest too! Now you math people out there just have a whole lotta fun with that challenge 😀
all you guys are making this hard it is just teaching a good lesson and you are turning it into something complicated. I thought it was a wonderful lesson. And remember the rule if you dont have anything nice to say dont say anything at all. think…just think…would you like it if people were saying things like this to something you post on the internet to teach a lesson and help the world? i sure wouldnt. just be careful what you say and the world will become a better place! thanks! 😆
ya i totally agree with izzyz. i loved this penny lesson. i just wish someone gave me that choice so i could really do it. =D 🙂
but where is the BANK that this is happening at? Cause it means nothing if it can’t be done realistically!!!
Real answer if you are receiving a penny a day double for 30 days.
$10,737,418.23
If you are just doubling the number for 30 days it’s $5,368,709.12.
Most people use this in terms of, “Would you take a million $ or a penny a day double for 30 days. You have to add all the totals together. It is .23 not .24 on the ending. .24 would be if you double it again. But that isn’t the answer because you didn’t receive the first penny twice.
There’s some knowledge for you.
open your calculator and hit .01*2 then that(.02) times 2, then hit enter for every day in the month, 30 times=5,368,709.12 31=10,737,418.23 after a year (365 days) the total is 1.989292945639147 to the 85th or 19,892,929,456,391,470,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 that is the right answer for all three questions above, i have no idea how to say this number i just now that 19,892,929,456,391 is 19 trillion 892 billion 929 million 456 thousand 391 then you add whatever 470 with 66 zero’s behind it is
😯
Juza,
19,892,929,456,391,470,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 is pronounced 19,892,929,456,391,470 megaseptatribazillion!! 😎
Ben,
You are a perfect example of why so many countries in this world are passing the US in education. Your obviously severely short attention span didn’t allow you to read more than a few lines of this thread, and then you opened your mouth, and promptly put your foot in it.
So sad…
Use this in an ecomonics lesson…thanks
Umm, guys, It’s called exponential functions.
ever heard of it? yeahh.. Learned it in algebra 2 as a high school student.. 🙄
I was looking for the wording of this scenario to show my 7th grade students the power of exponential growth as it pertains to bacteria growth. I worded it the following way to avoid the confusion between exponential and compound that apparently many of you share with 7th graders…
“Would you rather have a magic penny that doubles in value every day for 30 days, or one million dollars handed to you in 30 days?”
Formula is 2 to the power of (day1). In 30 days you have $5,368,709.12. Read post 28 for the correct math.
I totally disagree with this. One penny doubled daily for 30 days would give you only $.60 total or $.59 if it doesn’t double until the second day. I would take the $1 million in hand. Only if the total is doubled daily do you get the $5 million answer. Everyone reads this incorrectly. My dad gave me this puzzle when I was a child and I am now in my 60’s. This puzzle was given to my grandson, in a class today and he got the $5 mil answer. I had to break his heart and tell him it was wrong! Sorry folks. It is all in how the puzzle is written.
the question I had, is if I doulbe what I saved from the prior day and in 31 days I would have to add 10,737,418.24…how much would I have saved all together? and what is the formula to figure this out?
how much dollors is this???? 😕 ❓ 😐
Whoever says that you add the 1 to 2 to 4 is incorrect. What’s happening is that you have one cent. The next day another cent is added to make 2. The next day 2 more are added to make 4 after that 4 added to make 8. You are not adding these all together. Your sum just becomes doubled to make the next sum.
With 126 comments thus far, maybe this is already said. But, it’s all a moot point if you die on the 10th day. Take the One Million, enjoy it like there’s no tomorrow. If you can’t sustain yourself on a million dollars, you sure as hell can’t do it on 5 million.
Figured out the formula
.01*2 to the X power
X= number of days
watch
.01*2 to the 1st= .02
.01*2 to the 2nd= .04
.01*2 to the 3rd= .08
.01*2 to the 30th = 5,368,709.12
I am 12 years old and i figured that out!!!!!!!!!!!!!!!!!!!!
I messed up on the equation above.
X=number of days minus 1
If you want to look it where the total adds up, then you double the answer and minus .01
any body know what 3.75766813 Ã— 10 to the 107th power looks like?
.01*2 to the 364th=3.75766813 Ã— 10 to the 107th
364+1= 1 year
Dear Margaret (who wrote on Feruary 3rd comment #123),
My dad gave this puzzle to me and I got .60 cents and he told me I was wrong. The way he told me I thought that I went 1 pennies 2 pennies 3 pennies and so on. He told me that it doubled every day. Today I figured out in about 30 minutes the formula for X days.
$$= .01*2 to X1 power
You have a new job. You are offered 1 million dollars for the month or one penny on the first day, and that doubles each day. The formula is (.01*2^X).01
Where X is the number of days.
Since the total is doubled every day at the end of 30 days the grand total would be $10,737,418.23
That is exactly what I said
except I simply made it so they didn’t add up together
I remember seeing this in school. one of my teachers showed us this on blackboard. what i want to know is how i can actually do this in real life. i would love to multiply money like that.
A lot of people are still wrong. The original and the widely accepted notion is the investment ROI concept. In this penny doubling parable, the principal is 1 cent and ROI is 100%. It is principal plus ROI. Not another 100% created out of thin air and you add all the results up. No. The original concept was principal plus ROI. You start with penny and on second day you have a total of 2 cents; 1 penny as principal and 1 penny as ROI. And this same reasoning applies all the way down through 30 days. That is the original intent and teachings of this. The universal investment concept of principal + ROI. So second day, total is 2 cents and third day, total is 4 cents. Investment model is the example here; not multiplying pennies and then just adding all the lines up. Principal + ROI!
Ya, and another thing. Even on a totally physical level. You are doubling an entity which is a single penny everyday. Even on this simple physical level, on second day, you will have 2 cents, not 3 cents. Physical item is doubled everyday. First day, you have a single penny, it doubles and on second day, you have 2 pennies. Why do some people insist on adding up all 30 lines of data? That was not the original concept… not 2 cents arising out of thin air to add to your first penny. Your first penny is doubling… second day you have a total of 2 cents. If you say it is 3 cents, it is not doubling, it is tripling. The concept is 100% returns on principal, not 200% and continually rising returns. It is 100% returns on your growing principal. On second day, your principal is 2 cents.
Total is not doubled everyday. The lesson here is again original principal plus ROI of 100%. Why do some people insist on adding up all 30 lines? You are not adding up all 30 lines. Day 30 principal is what is stated on line 30, not the sum of lines 130!
GOOD HEAVENS!!!!!!!!!!!!!
🙁
I know you double each day, but do you add to the day before? 🙄
@vindy
Betting on horses, sports, etc.
I’m retiring in 24 months with this same exponential growth concept. Except it’s $1.50 times 3 and they all do the same to give me $117,000 per month retirement income within 18 months. I’m in my thirties! The answer is $5,368,709.12. I know because I’m getting a pay check based on this plan in real life and not just in a math problem.
lol
My question would be who would want to carry all those pennies to the bank and count them out…
@travis: I would want to carry them….I’ll count them because at the end of the day its gonna be all worth it… 🙂
But just one question is all of this possible in real life?
Too bad no one have a clue as to how to actually duuble a penny each day for 30 days. I say this is impossible for a none billionaire person. The reason I say this is because if it was possible we would have more rich people than we do.
Just my thoughts
WOW 😯 , what a rough crowd!!! 🙄
I originally heard this years ago. Some one asked me “What would you rather have? A million dollars right now or I will put this penny in a jar and I will double the amount in the jar every day for 30 days and then give it to you.”
So anyway I understand the lesson, but I live in the real world and over the course of 30 days a lot can happen. If your luck is like mine is 70% of what happens isn’t gonna work out in your favor. My luck on the 26th or 27th day the Federal Reserve would discontinue the penny all together so that all I would have would be a pile of Zinc. Hummm, I wonder how much zinc is worth ❓
So anyway, I hope you all get rich quick! My plan is slightly more complicated. I would like to have the Million dollars now please. So that I can live very comfortably for many years on $999.999.99. During these years of comfort I plan to spend all my time trying to figure out how to get that last penny to double ❗ ❗ ❗
➡ My final thought … If I had a penny doubled for every post in this thread, would I have enough for a cheeseburger and fries ❓
OK that last post was my 1st penny ❗
So now here is my 2 cents … If anyone has bothered to follow this thread, I would like to make an announcement. In exactly 11 days this topic will have reached it’s 5th birthday. CONGRATULATIONS ❗ ❗ ❗
For those of you who think it is impossible. Any thing is possible!!! Perfect example: Who would ever dream it possible for so many people to either reword or argue about the wording of the same basic principle “Double a Penny” and spend 5 years doing it ❗ ❗ ❗
Anything is possible, but take care, the “Pigs on the Wing”.
well where can a person find pennies to go about doing this project?
I don’t know what is worse…the fact that there are 143 comments (144 including mine) about such a trivial topic, or the fact that I was bored enough to read every single one of them.
look let me tell u this
you:mom get me nothing for christmas
mom:why you have to have something
you:ok just give me a penny
mom:thats not a very good christmas
you:ok if u want to get me something just give me a penny for 30 days and double the price everyday ok
mom:ok if thats what u want
you parents will think ur not that smart they will just keep giving u money until the realize hoe much money u have so give it a try at how it might work it might not just hope your parents ARE NOT that smart 😉 😆
I just lost this bet! I now owe someone for the 30 days (almost 11 million)he did take off one day to make it a 30 day month, but I also owe 3000 sessions of sex. OMG 😉
Can’t believe all of the comments here.
I used to do this with my 3rd, 4th, 5th and 6th graders as a BASIC computer program in the early 1980’s! Then, when the Spreadsheets became available, it made it even easier!) Just a simple formula in one box, and then fill down function, and Eureka! Joi! The kids did this with nickels, dimes, etc. Ask the kids who attended Edgeworth Elementary School in Sewickley, PA, USA! 😉
Social Good Doubling / Tripling effect : the Power of Three
Day 1 $0.02 0.03
Day 2 $0.04 $0.09
Day 3 $0.08 $0.27
Day 4 $0.16 $0.81
Day 5 $0.32 $2.43
Day 6 $0.64 $7.29
Day 7 $1.28 $21.87
Day 8 $2.56 $65.61
Day 9 $5.12 $196.83
Day 10 $10.24 $590.49
Day 11 $20.48 $1,771.47
Day 12 $40.96 $5,314.41
Day 13 $81.92 $15,943.23
Day 14 $163.84 $47,829.69
Day 15 $327.68 $143,489.07
Day 16 $655.36 $430,467.21
Day 17 $1,310.72 $1,291,401.63
Day 18 $2,621.44 $3,874,204.89
Day 19 $5,242.88 $11,622,614.67
Day 20 $10,485.76 $34,867,844.01
Day 21 $20,971.52 $104,603,532.03
Day 22 $41,943.04 $313,810,596.09
Day 23 $83,886.08 $941,431,788.27
Day 24 $167,772.16 $2,824,295,364.81
Day 25 $335,544.32 $8,472,886,094.43
Day 26 $671,088.64 $25,418,658,283.29
Day 27 $1,342,177.28 $76,255,974,849.87
Day 28 $2,684,354.56 $228,767,924,549.61
Day 29 $5,368,709.12 $686,303,773,648.83
Day 30 $10,737,418.24 $2,058,911,320,946.49
thanks this helped soo much now i get itt …!! 😀
According to the first post, you will only get the one penny doubled.
As posted “a penny doubled every day”
A penny. Not all pennies.
NOT the sum amount.
If interpreted like this u will only get 31 penny at the end of day 30.
If a djinn came and offer someone this for the price of one testicel. I wouldnt feel too greedy.
Othewhise, as a mathematical problem, I would say Mim Bizic had the correct solution
ok what if a man want to know if his sun is smart or greedy he gives him the option to choose between millon dollers or i penny and double for 30 days what does he choose??
Lost over $200 at a bar because I bet my friend i wasn’t true…..I lost
Double a penny work don’t put a time on your double goals if you do 24 mo. is a good time frame.
So if I apply this to my business..network marketing, Day 12 let’s say that is Month 12. I would have 2048 distributors. If those 2048 distributors each had 200 volume a month, at 5% residual income I would be earning $20,480 a month.
Now back that up with a medical breakthrough product and the possibilities are endless.
omfg!!!!!!!!!!! all of you stfu!!!!! the guy was just trying to make a point about this because people have become too lazy to do the math on there own!!!!!!!! you may understand it one way, the next guy may understand it the next but nobody cares whether or not it is double the amount you have or giving you double the amount you received!!!!!!! 👿
well, whoever said this was a bad thing go take a dump cuz this guys a genious. all hes trying to say is never take a shortcut in life. but apparently you guys dont get that. 😀
If the question is ‘Which is more?’ then yes you are correct.
If the question is ‘Which should you choose?’ there is more than one answer.
For example: cash now is better than cash later. Will you really get the 5m? A guaranteed 1m vs a speculative 5?
What if on day 2 you’re given 20 days to live because you’ve been diagnosed with a disease that would cost a million dollars to cure?
this was good for my homework but i need help again in my homework so please help ,me again here it is would you rather have 1p per day doubling each day, or £1 per week doubling each week for a year? show me yuor working out blow please ok
please help me 🙁
i need help with a problem, i need to consume 4900 grains of rice, i need to start with 2 grains on day 1 and double each day until i get to mid point at 2450 then work my way down ending with 2 grains on the last day.. eg. 2,4,6,8………8,6,4,2. question is how many days it take?
has anyone ever done the double penny for a day and made over a million dollars?
Actually yogi your comment doesn’t make much sense but since you inquired that screw you all 😀
For the “adding it up” crew… This is called tripping.
B Shan: how many cookies do you have in your lunch box?
Alan: 1
B Shan: ok how many should I give you so that you have twice as many as you have now?
Alan: 1 because 1+1=2.
B Shan: very good. Now let’s say you keep that cookie and I give you twice many cookies as you have now in addition to the cookie tha you have. How many cookies will I give you? How many cookies will you have?
Alan: you will give me 2 and I will have three since I keep what I had and add what you give me.
B Shan: so if you started with one and now have three do you have double the original or tripple?
Alan: Tripple
B Shan: very good Alan. Good luck getting to find some one to continue doubling or trippling your cookies cause I cant afford it.
Semantics.
Commenters on semantics are right and he way it is worded it is .60 cents but the intent of he post was obviously closer to the penny in a jar analogy than the actual .60 cent wording. The assumptions of adding it up ad based on. It understanding “double”. If you want to earn this kind of money you have to be ome a loan shark, but your more likely to end up breaking a lot of legs before you make this kind of scratch.
If this kind of money. Oils be made in real life (assuming the 5 mil+ answer) then we coin onto he the trend beyond 30 days and lay off National debt. So that oh children could stand a chance in the future.
i have wondered how i can make that a reality. anyone have some ideas?????
I’m with the 12 year old. Way to go Mitchell!… and the others… that note it says… a “penny doubled everyday for 30 days”… and does NOT say a penny doubled plus the original investment. One penny doubled is 2!… not 3… that would be a penny double plus the original investment.
Regardless, it really doesn’t matter… it’s the MESSAGE which a young lady so eloquently put it above. If you persist in doubling money, efforts, whatever IT is… it will pay off larger than the quick bandaid approach most people’s minds to to first! Why most people, roughly 9798% of our population, are broke. Varying definitions of broke, but none the less broke.
To Christine with the 85 job… you could ditch it if you do some research. Find a good network marketing company… one with integrity… and a binary comp plan… and you can double much more than a penny… and help others do the same… and many people can win from utilizing this principle of duplication… the principle of hard work and dedication. Teamwork makes the DREAM WORK! Or you can stay asleep in the American Dream like 9798% of America. That’s why they call it the American dream… you have to be asleep for it to work! Check out what Robert Kiyosaki, Donald Trump and Warren Buffet are saying about network marketing and right now! It’s prime time… for us to take control of our lives!
This was an entertaining and educating read and thank you everyone for your part! Good evening!
Vanessa Wilkerson, Dallas
i would have never thought this would cause so much debate, the correct answer would be decided based on how you phase the question because “The scenario was 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?”.
A penny doubled for thirty days, would mean day 1 of the 30 days is actually a penny doubled = 2 cents ($0.02)plus doubling every day for the next 29 days. Meaning the actual total is $10,737,418.24
But to take it one more step the question was “which would you choose?” not what is the total….LMAO 🙂
I’m with the smart people who said they’d take the million dollars because you never know what might happen in 30 days.
Like:
— It turns out the doubling thing was fake, they never meant it. Take the million, and you’ve got it.
— Maybe they meant it, but they didn’t think it through, and once they see what’s going on, they skip town. Or just run out of pennies to give you.
— Or, as someone said, you drop dead waiting for the rest of the pennies.
Be smart. Take the million.
Sometimes pragmatics take precedence over math. 🙂
This is just another attempt to make a misleading situation out of the ancient “a grain of rice on a square of a chess board puzzle”. On square two, two grains of rice; on square three, four grains of rice. You continue doubling it every day for all 64 squares. Once the 64th square receives all the grains due to it, the question asked is ‘How many grains of rice do you have?’. Hence the purpose is to give the complete number of grains of rice that are on the board.
In the above example, on day 30, $5,368,709.12 is that day’s result. The total of all the money from day 1 through day 30 is $10,737,418.23. If the question were only ‘How much money do you make on day 30?’, then the $5M dollar figure would be correct. But the question implies you can choose the $1M now or the TOTAL of all 30 days’ worth of doubled amounts. Take the column of numbers, paste them into an Excel (or some other) spreadsheet, total downward from the box (cell) containing the $0.01 (day 1) to the box containing the $5M figure (day 30) and your total amount of money is $10,737,418.23. It has been obvious from the start that the ‘doubled amount every successive day’ plan is the right choice, regardless of the theoretical losses or interruptions.
In case you’re curious about the grain of rice answer, the 64th square would hold 92.234 quadrillian grains of sand, but the TOTAL number of grains on the entire board would be 184.467 quintiliian.
It sort of follows the old trick question about a lilypad doubling in size every day, and in 28 days it will cover the entire lake. How many days does it take to cover half the lake? 27 days, because it DOUBLES in size EACH day.
Just because day 30 nets you only $5.3 million it doesn’t mean you get ONLY the 30th day’s worth. You get the total amount of money from ALL 30 days, or $10,737,418.23.
And the question was worded wrong: it’s not ‘the penny’ being doubled each day — it’s the previous day’s total being doubled each day.
Lovely old hypothetical, this one 🙂
Every time I’ve seen this question in the past it was not a trivia about investments, it was a brain teaser about receiving money. Hence, it’s all free money since it’s not an investment.
That being the case, you’d end up with day 1 + day 2 + day 3 + day 4 etc… or .01 + .02 + .04 + .08 (etc…) + the five million at the end… or close to ten million dollars.
In spite of the poorly worded question, that’s how the original brain teaser was worded and that’s the solution to it.
Of course it is just a hypothetical, as nobody can offer the penny deal. Even most millionaires would go bankrupt in the middle of the month (though the gift recipient would be happy LOL)
I remember when I was a child back in the 80’s I had a book that said the doubling pennies would add up to two million at the end of the month. So my dad and I got on our Commodore 64 to write a program to figure it out… and the program came up with the ten million number and we wrote to the publisher about it.
is iwanto dobule the money in 30 dayes i well invest 1000
Here’s where the semantics really come in.
The first time I heard the whole “Penny that doubles itself for 30 days” idea was in it’s supposed original parable form: A young kid was approached by a sheep owner looking for a shepherd. The owner had to go away for a month, and was clearly a miserly creep out to shave every penny that he could. The kid, however was smarter, and offered the pennythatdoubles deal. The sheep owner, too greedy to look past the humble, lowcost offer that it seemed to be, accepted and left.
Where the parable part comes in is this: At the end of the month, the powner came back and the kid handed him the bill. Instead of paying up, the owner flew into a rage at having had his own greed and stupidity used against him and killed the kid.
I guess the moral of the story is, “Math and Stupid people don’t mix.”
WRONG!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 👿 👿 👿 👿 👿
I am literally appalled at the stupidity here. Add them together? Start with .02 on day one? 30th power? My gosh, no wonder this world is messed up. 🙄
so i got it… instead of doubling a penny a day for a month, double it every 18 days you’d still have the 5 mill in 540 days 🙂 so you only need to make 4% of your penny compounding the investement every day which is very easy . the trick is called sports arbitrage, where you get maybe 5 sports arbitrages a day at 4% 2 sites that are great is mathbet and rebelbetting… but they do have a user fee of over 150 a month… but what the heck 🙂
Solve either problem, or whatever problem you like.
Starting with 1 cent and adding the total to the total each day after day 1:
The sum S = 1 + 1 + 2 + 2^2 + 2^3 + 2^4 + … + 2^28
2S = 2 + 2 + 2^2 + 2^3 + … + 2^29
S – 2S = – 2^29
S = 2^29 cents = 5, 368, 709. 12 dollars
Starting with 1 cent and each day thereafter adding double the total of the previous day:
The sum S = 1 + 2 + 2^2 + 2^3 + … + 2^29
2S = 2 + 2^2 + 2^3 + … + 2^30
S – 2S = 1 – 2^30
S = 2^30 – 1 cents = 10, 737, 418. 23 dollars
Why not start with 1 cent and each day thereafter add double the total of all of the previous days?
Let S be the sum.
S = 1 + 2 + 6 + 18 + 54 + 162 + … + 30th term
S = 1 + 2 + 2(3) + 2(3^2) + 2(3^3) + … + 2(3^28)
3S = 3 + 2(3) + 2(3^2) + 2(3^3) + … + 2(3^29)
S – 3S = 2(3^29)
S = 3^29 cents = 686, 303, 773, 648. 83 dollars
Stunning story there. What occurred after? Take care!
Thanks for sharing your info. I truly appreciate your efforts.
A Penny Doubled Everyday cool math games
i am interest in games
😉
My son and I saw this played out on the Electric Company childrens TV show about 20 years ago: it was fascinating to me then and still is however what I would like to know is how can this math concept be applied in ” real” life. All answers welcomed. Thank you for your time 😳 😳
i want to double the money
ok so I guess we are all screwed now that the pennies are no longer in circulation .. does anyone want to calculate how much 5 cents a day doubled everyday works out to 😆
The 200th comment and the first in 2015!!! 😈 I should get the money as a prize 🙂
Where is the link to start earning in that like site?
You said a penny was doubled every day….You didnt double the penny on day 1, you doubled it on day 2. The correct amount is 1073741824 pennies…converted to dollars is $10,737,418.24
Present value is always at time 0, or in this case, day 0. Another way to think of this is you are given a penny at the beginning of day 1 (end of day 0). At the end of day 1, you will have $0.02. At the end of day 30, you will have $10,737,418.24. The equation is (2^30)/100. How you have it shown, one of the following is occurring. You receive $0.01 at the END of day 1, and then you would have $5,368,709.12 at the END of day 30. The other case is you receive $0.01 at the BEGINNING of day 1, and then you would have $5,368,709.12 at the BEGINNING of day 30. Both of which are incorrect in a time value of money calculation.
This is simple math and half of you want to argue with the answer… Especially Jon… I bet you get lost a lot!
Jon, finally some simple logic that deals with an exponential function in general 2^x. All these people ranting about trivial crap. I agree that in a 30 day example, the formula is (2^x)/100, where x = 29, since you have to discard the initial value of 1, obviously.
This is a high school math problem in geometric series. The only answer to this specific geometric series problem is 2 raised to the (n1) power. That is all. If you want to further calculate the total in terms of Dollars, simply divide by 100. It’s really that simple.
I first saw this math “riddle” in my 7th grade computer science class in the early 89s. The teacher was making a point about the binary numbering system (that is Base 2).
The deeper mathematics in this example is that a geometric series has a fixed ratio between all terms in the series. In this Penny riddle, the ration is 2…as in Base 2.
The author is correct. Again, a simple geometric series problem. I can’t believe the number of responses to this post!
Clue to answer is in the wording of the question; a penny doubled every day for 30 days, That’s $.01 @200% compounded daily for 30 days= $5,368,709.12.
If it was worded: a penny doubled every day and for 30 days then you get $10,737,418.23
my savings are at day 22. plan to be at day 24 by end of 2016
so instead of doubling it every day after day 24, I plan to double every year. so in 78 years I will have $10,737,418.23.
This is so cool! If only my boss would do that for me…
I think people should not name call and take this as a healthy academic debate (or just fun). Just the exercise in semantics alone is rewarding if you take it right! I had my brothers 5 year old daughter pull this on my brother(worded clear). He got mad at day 11 when the total given reached 20.47. Our total would have been 10,737,418.23. He gave her the money to day 11 and a movie and she let him off the hook.
Rao “was a math major and programmer”
How after so many days do you get hundreds of dollars to put in everyday? From $300 one day then $600 the next where’s that money coming from?
The goal is to take what ever you have little or much and double it till you get to 10.7 million.
you would need to find ways to take the money you have and invest it till you double it even if take you a day, a week or months. the goal is to double your money.
get creative – I bought a STILH hammer/drill on a garage sale for $100 and sold you for $385 for $285 profit. My goal is to save enough money to buy a buy fix upper house and flip for bigger return.
All you need to do is, when you’ve doubled up to the 30th or 31st time, double it once more and subtract 1, so to get the final total of all.
so is there an institution we can invest in and have it doubled every day?
If you have the ability of getting $1million in just day one, that proves you have the ability to make another million on day 2 from elsewhere. So why not take the $1mil and make another 30 $1mil + $2mil + … yourself? (You would have $2million on day 2 and it doubles IF YOU HAVE THE ABILITY.)
Moral of the story: know your place. If you not worth the $1million, then choose the second method and just be happy about getting what they give. If you have the ability, then take the money from day1 and earn it yourself for the rest of the month
Formula is (.01*2^(n1)) or .01*2^(301)
The the answer from the original post is right.
What if it is February (no leap year) ? You only get a paltry $1,342,177.28
Bah humbug !!!!
So, If I double this particular penny every day, I would have 30 extra pennies, plus my original one. I have $0.31 literal dollars. If I can sell my magic penny for more than $122 for its BanachTarskiesque metallurgical properties, then I would have even more dollars. But, that value is dictated by the market.
Here’s a trick I learned in college math pertaining to the sum of geometric progressions which this is. A geometric progression starts with one number and keeps doubling at each entry. Like 1, 2, 4, 8, 16, etc. Or 3, 6, 12, 24, 48, 96, etc. To find the sum of any geometric progression, just double the last entry and subtract the first. So in the problem given you take the amount earned in pennies on the 30th day, double it and subtract the first entry or one penny. To find the amount in dollars of course, you must divide by 100.
Based on these answers 90% of you probably failed math once it got to word problems lol. Just kidding. But really, the trick is to READ THE QUESTION without adding or taking away from it. The question was “a penny doubled every day.” That’s only $.60cent because you would start with .2 and add .2 for 29 more days. Now if it was worded that you start with a penny then double the penny every day, you would have .59 cent because the first day was .1cent not .2cent A separate question would be “if you doubled what you put in the day before” by the end of the week you would have a sum of $1.27
ANOTHER question would be “if you doubled you total sum every day, starting with a penny.” You would have $7.29 at the end of the first week. Do the math for yourself. There are many way to get different answers when you’re asking different questions. But the technical and correct answer to THIS is .60 cent. I know that wasn’t the point of the post… But in actuality it was because it’s all about encouraging people to think it through. Years later you still have people thinking. Thats a GREAT post!
The original question was “What would your monthly salary be if your rate was 0.01/day the first day, and it doubled each day?” That’s what the math above is showing.
This is interesting to consider, but so is the question of who would win in a fight between Batman and Superman. How often do people get double their money back except with really risky gambles in Vegas or the stock market? For every success story, there are 2 to the power of 30 that lose that money or grind it out like the majority of us. It would take around 10 years to double your money at around 89%% interest. That’s a lot different than having it double every day…
Thanks William for your truly obvious insight!
Addiemil, you are completely wrong of course and your math skills are atrocious!
A single penny doubled every day is only .60 cents.
If I say to you I will meet you at the corner with a penny every day and double that penny you will get 2 pennies per day times 30 days for a total of 60 pennies.
Now if you say we are going to double the number of pennies each day then you are compounding the pennies and it is no longer a PENNY a day it is multiple pennies per day.
You are all great. But if I were to be asked the question, I would take the million dollars now. It’s all in the NOW. Tomorrow is never promised. Sure we can hope for 30 days.. and that is a gamble. There are a lot of things I can do with a million dollars NOW. LOL
NOTE: A bird at hand is better than 2 in the bushes..
Wow so we all know no one has the answer
Technically, there’s a semantics argument and we’d have to define the problem.
The original problem, as worded, was:
The scenario was 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?
What does “a penny doubled every day for 30 days” mean?
It COULD mean, 2 cents (a penny doubled)every day for 30 days.
That’s 60 cents.
Or it COULD mean, every day, you’re doubling your money.
That’s $5,368,709.12.
Or it COULD mean, every day, you receive double the previous day’s haul, not including what you’ve already received.
That’s $10,737,418.23.
The problem is that the question leads to another question.
What do you mean by “a penny doubled every day for 30 days”?
Because one could argue for many definitions to that word problem.
Of course, if we assume any of the larger numbers, you’re going to have many logistic issues. You’re getting paid in pennies. Where are you going to store all these pennies? You might have to hire people just to count them all. You’re certainly not going to be able to drop them all into a Coin Star. There are too many! However, with that large a number of pennies, if you’re very, very patient, you’re likely to find some valuable ones in there. Maybe a 1909 S VDB, or some other rare and valuable pennies.
5368709.12
(2^29)/100
Okay so if you double it “everyday”.the key word being everyday. you would receive a penny the first day and then another also on the first day. because its doubled everyday therefore it would be about 10+ million. that’s the catch though its about paying attention. it says everyday not everyday after the first day but in general every single day. I’m probably wrong but in my theory it would be the correct way of doing it. Because if you don’t double the first penny then your not doubling the first day. your doubling the second and so on making you loose one day of pay. witch could make a 5 million+ dollar difference my mind works weirdly. so its probably wrong but that’s my theory on how we get 10 mill + and others get 5.
The question said 30days&answer is over 10 million when add all thirty days together it’s not that difficult
Wayne? I’m wrong because YOU don’t understand math? I LITERALLY gave you EVERY scenario of how people could come up with different numbers for this question. The reason people come up with different numbers is because they interpret the question differently. I cannot argue with you or debate with you if you don’t understand simple math and you honestly feel like my answer was wrong. It’s entertaining to think that someone things like that but it’s truly sad if you are an adult and think that my whole statement was wrong. I would like you to be my boss and pay me a penny a day doubled if you think it’s 10 million dollars LOL I’ll take my monthly Penny doubled salary and tell you thank you, have a nice life. Read how Charles broke it down. Maybe that will help you understand better.
I have yet to master my #onemillionpennychallenge. I think I’ve got up to 13 to 14 days. Thank you for doing this for us. I am doing this challenge for research for diabetes.
.01×2^(29)=5,368,709.12×2.01= what it all adds up too.
But if you start with a penny and double it for 30 days you would have 2 cents on day 1 + the penny you started with, good luck
To those who were using a scientific calculator, it’s not 2 to the 29th because you are starting on day one with one. 2 to the 29th assumes you are starting the first day with 2. That’s the reason why it’s the 30th day not 29 when you get the $5,368,709.12.
The reason people are adding it all together is because it’s an extension of the story of the man that invented chess. For payment he asked for 1 grain of wheat on the 1st square, 2 on the next, 4 on the next, then 8, and so on… The king (who offered payment) laughed at his meagre request & agreed immediately, later realised that with chess board having 64 squares the total number of grains of wheat came to: 18,446,744,073,709,551,615!!! Or around 1,199,000,000,000 metric tons (or tonnes) 1,645 times the total global production of wheat in 2014! Just imagine if he’d asked for pennies instead! I think I could survive on that ?
A penny doubled everyday for a month is 60 cents for an average 30 day month. Lesson one Read and interpret.
This million dollar question has been around for many decades. Does anyone know of it’s origin? The comments here are quite funny.
The way i learned this was, immedate gratication 1 million today vs. the mirical of componding intrest starting with a penny that doubles in value for 30 consecutive days. Basically, make your money work for you, not work for your money. Great article and look forward to reading more from you in the future.
Dear World—I got tired of reading all of this, so, I decided to add MY 2 cents.
If you double your money every day by giving it to someone else to double it for you (commonly known as “Investing”, You must remember that you don’t have it any more. Therefore you cannot add the new amount to the old amount that you don’t have.
But, if you are getting double the amount of yesterday’s gift each day from someone else, then you can add that to your pile.
I am not a math wizz, but I listen to the instructions or the questions carefully.
I don’t know many people who can put $1,000 a day away never mind doubling it!
It comes out to way more than $5 million! If you are actually receiving the amount every day ss it doubles, then you need to add all 30 days together to figure out the grand total is of what you received!
literally everywhere I look, I am shown how the penny doubled everyday for 30 days works mathematically – but NO ONE has said WHERE / WHO is doubling it for you!? Who has actually had success with this, and where did you invest to make it happen!?!? The math is great, but the $5,000,000 is what we obviously want!
Also, If I were to be asked if I wanted a million dollars today, or a penny doubled everyday for 30 days, why would I not take the million dollars and start with doubling that everyday for 30 days!?
In reality a penny doubled everyday is really only $.02 every day… multiplied by 30 is only $.60. With the offer as it is phrased, and where as your math may be correct in formula, this isn’t a logically correct assumption.
It is “doubled every day for 30 days” which means it is doubled on day .01. So one doubled is .02.so on day one, how have 2 cents. On day 30, you have over 10 million dollars. It does not say “add double the amount every day.” It says “double.” So you take the number you have and add that much to it again, doubling it. You dont add all the numbers together, although it would give you the correct answer, just derived through the wrong method.
“Everyday“ one word, means something that is commonplace, for instance: “these are my everyday jeans.“ “Every day,” two words, means something that happens daily. For instance: “I wear my everyday jeans every day.“ There is a difference, though no one seems to observe the simplest spelling and grammar proprieties anymore; not even writers or editors. What happened to standards?
After all of this arguing, I can’t believe everyone missed the elephant standing right in front of them. Assuming the author did the calculation and the total was 5,386,709.12, the author then goes to claim that this equates to “5 million Dollas”. What every forgot is that the calculation was done with pennies, not dollars. So the result is 5,368,709.12 PENNIES. You have to decide this number by 100 to get dollars, which equals only $53,687.09. So even if the author is right about his calculation, TAKE the million.
I think everyone is missing the most important part of the document. Regardless of how you calculate it, the question everyone should be asking is, “How do I take my initial Penny, and double it everyday?” PERIOD! I have lots of pennies. If like someone to teach me how to double each one of them, initially, and continue to do so daily.
i am confusion _ xD
hello
The 5mil is correct.
People are just being greedy. 🙂 It says DOUBLE….You don’t get to Keep the money and double new money. (although that would be nice).
I mean theoretically if you add it up you would get too much money if you get a penny doubling every day from the previous day and you owe the money to a person unless you are crazy enough to mine the asteroid Ceres and keep all the money to yourself. 7.44e+20 is the formula of how much money you would get and you would be completely fine
So, if a person caught the corona virus on jan 1st, and each day the number of infected people doubled because every infected person infected only one other person.How many people would be infected by december 31st.
@john Campbell
To figure this out here is the calculation.
1×2×300×1000÷10√9100,000,000×30√÷10+100√6
Run that calculation and get back to use with the results.
i guess i should be thankful for your response.
These comments have given me the answer to why so many are in financial ruin, living pay cheque to pay cheque. Thank you so much! I stand back, looking in at a situation and think “do I want this or not?” I most definitely do not want this. I will stay my course away from this comments!
These comments have given me the answer to why so many are in financial ruin, living pay cheque to pay cheque. Thank you so much! I stand back, looking in at a situation and think “do I want this or not?” I most definitely do not want this. I will stay my course away from this comments!
How many days would it take you to reach over 9billion or the current world population by handing out a penny to someone and every additional person takes a penny from the over nine billion pennies and hands them out … more people to receive one the more people handing out one to others as well? Take a month, two months, three months, four months, five months!
If it’s doubled could you say once you get to two cents
You go
2×2 then 4×4? And 16×16 wouldn’t that be doubled the same way? Did someone already say this? I was too lazy too read a thousand comments
What about
4×16 16×64?
That’s really doubling
This is a geometric sequence problem.
Nth term= 0.01 x 2^(n1). The original post is correct.