Ben is an investment writer. He's been managing his own pension and ISA portfolios for a number of years. His approach aims to balance growth and income styles of investing.
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If a very kind stranger offered you the choice of a million pounds today, or 1p doubled every day for a month, which would you choose?
I’m sure many people would take the £1m, and I can’t blame them. After all, that’s the sort of money that could fund a luxury round-the-world holiday. And there might still be enough money left over for a single Class A share of Berkshire Hathaway, which currently stands at $537,780!
But would taking immediate millionaire status really be the best option? Or would the delayed gratification route ultimately prove more enriching? Let’s find out.
Wheat on a chessboard
First, I should note this mathematical exercise has been formulated in different ways for many centuries. Probably the most well-known involves wheat on a chessboard.
This is how Wikipedia expresses it in textual form: “If achessboardwere to havewheatplaced upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the finish?“
The answer is 18,446,744,073,709,551,615 grains of wheat. Wow!
However, many readers will be aware that a chess board has more than double the amount of squares (64) than a month has in days. So how would much would 1p doubled over 31 days be? Here are the calculations.
Day
Amount
1
£0.01
2
£0.02
3
£0.04
4
£0.08
5
£0.16
6
£0.32
7
£0.64
8
£1.28
9
£2.56
10
£5.12
11
£10.24
12
£20.48
13
£40.96
14
£81.92
15
£163.84
16
£327.68
17
£655.36
18
£1,310.72
19
£2,621.44
20
£5,242.88
21
£10,485.76
22
£20,971.52
23
£41,943.04
24
£83,886.08
25
£167,772.16
26
£335,544.32
27
£671,088.64
28
£1,342,177.28
29
£2,684,354.56
30
£5,368,709.12
31
£10,737,418.24
The final figure after 31 days of doubling is £10.7m!
With the benefit of hindsight, then, you’d be kicking yourself if you’d snapped up the initial £1m on offer.
Using compound interest to build wealth
Unfortunately, it’s not realistic to expect my money to double every day (or even year). But the good news is that it doesn’t have to in order to reach a substantial sum. Indeed, countless people have generated huge wealth at far lower annual rates of return than 100%.
Billionaire Jim Simons, the founder of quantitativehedge fund Renaissance Technologies, compounded money at66% annuallybetween 1988 and 2018. That is thought to be the greatest investment record on Wall Street.
Warren Buffett‘s long-term average annual return is just under 20% per year.Yet he is among the wealthiest investors alive because he has been compounding such returns since the 1950s. As we saw with the chess board example, the difference between 31 and 64 can be mind-blowingly enormous.
What this means is that the power of compounding returns can boost my wealth significantly over long periods of time. And that’s even with quite modest sums of money. For example, £500 invested every month with an average return of 10% per year would grow to £1m in 30 years.
Given enough time then, compounding can transform regular small amounts of money into a life-changing sum. But the sooner this process begins, the more wealth I can potentially generate.
Ultimately, choosing the penny doubling daily leads to more than five times the million-dollar alternative. Many consider this a lesson of the power of investing and long-term monetary growth, showing just what could happen if you commit to regular investing so that your money is working for you.
Now that you've read the fable, you can see the choice is pretty clear: it's better to have a single penny that doubles everyday for a month, versus $1 million up front. This is because of the power of compound interest. If you took a single penny and doubled it everyday, by day 30, you would have $5,368,709.12.
On the very first day, the penny you have doubles to $0.02. Then it doubles again, and again, for 30 straight days. On the 29th day that it doubles, the penny grows to $5,368,709.12, much more than a million dollars. By day 30, it grows into an astonishing $10,737,418.24!
However, many readers will be aware that a chess board has more than double the amount of squares (64) than a month has in days. So how would much would 1p doubled over 31 days be? Here are the calculations. The final figure after 31 days of doubling is £10.7m!
On day one, we have one penny, and on day two, we have two pennies.On day three, we have four pennies, and on day four, we have eight pennies. This doubling pattern continues for 30 days. By the end of the 30th day, we have $5,368,709.12!
Five key ways to double your money range from a conservative strategy of investing in savings bonds to an aggressive approach involving speculative assets. The classic approach to doubling your money is investing in a diversified portfolio of stocks and bonds, which is likely the best option for most investors.
Frequently Asked Questions. How much money will I have if I double a penny for 30 days? At the end of 30 days, if you double a penny every day, you will have $5,368,709.12.
You start with $1 and then $2, $4, $8, $16…. By the end of the 30th day, you end up with $1,073,741,824! This is the power of compounding in action, and in this case, the rate is 100%, leading to staggering returns. (We provided a calculator at the bottom of the article that creates a table and a diagram.)
As each penny is $0.01, we need 100 pennies to equal a single dollar. This means we can find our answer by dividing 5 million by 100 to convert 5 million pennies to dollars. This means that we have $50,000 U.S. dollars when we have 5 million U.S. pennies.
Business investment: You could use £1 million to buy a business or invest in your own. This type of investment can yield great returns but requires extensive expertise and considerable time investment. Property: Purchasing property is another great way to increase returns on a £1 million investment.
A = 1 imes (1+1/1)^(1 imes 50) = 1 imes (2)^50 = 1 imes 1125899906842624 = 1125899906842624 pennies. Therefore, if a penny doubled every day for 50 days, the final amount would be 1125899906842624 pennies.
You might be amazed by how quickly your penny can grow into one million dollars. It can reach five million dollars and, then finally, on day 31, more than $10.7 million.
Introduction: My name is Nathanael Baumbach, I am a fantastic, nice, victorious, brave, healthy, cute, glorious person who loves writing and wants to share my knowledge and understanding with you.
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