Last Updated on 7 September, 2021 by Samuelsson

Assuming a genie just appeared before you and ask you to choose between these two options — giving you a penny today and doubling it every day for 30 days or giving you $1 million today — which one would you choose? The truth is, most people would choose to have $1,000,000.00 today. This begets the question: how much does a penny doubled every day for a month end up being?

A penny doubled every day for the 30 days that make up an average month would amount to $5,368,709.12. This is obviously more than the $1,000,000 offered in the other option.

Surprised? Let’s find out how that could be possible.

Calculating how much a penny doubled every day for 30 days would amount to

Now, if you take a penny on the first day of the month and double it on the second day and then continue doubling the value every day for the rest of that month (till the 30th day), how much do you think you will end up with on the 30th day?

You start with 1 penny and then, 2 pennies, 4 pennies, 8 pennies, 16 pennies…. By the end of the 30th day, you end up with $5,368,709.12! Seems difficult to believe, right? Well, this is the power of compounding in action, and in this case, the rate is 100%, so the staggering returns are expected.

Penny doubling table

  Day Amount
1 Day 1 $0.01
2 Day 2 $0.02
3 Day 3 $0.04
4 Day 4 $0.08
5 Day 5 $0.16
6 Day 6 $0.32
7 Day 7 $0.64
8 Day 8 $1.28
9 Day 9 $2.56
10 Day 10 $5.12
11 Day 11 $10.24
12 Day 12 $20.48
13 Day 13 $40.96
14 Day 14 $81.92
15 Day 15 $163.84
16 Day 16 $327.68
17 Day 17 $655.36
18 Day 18 $1,310.72
19 Day 19 $2,621.44
20 Day 20 $5,242.88
21 Day 21 $10, 485.76
22 Day 22 $20,971.52
23 Day 23 $41,943.04
24 Day 24 $83,886.08
25 Day 25 $167,772.16
26 Day 26 $335,544.32
27 Day 27 $671,088.64
28 Day 28 $1, 342,177.28
29 Day 29 $2,684,354.56
30 Day 30 $5,368,709.12

 

With this, you can see that if those traders on social media who claim to have a perfect trading system that is making ridiculous returns are actually making those returns, they would have been richer than Jeff Bezos trading for a few years. As Jesse Livermore would say: “If a man didn’t make mistakes, he‘d own the world in a month. But if he didn’t profit by his mistakes, he wouldn’t own a blessed thing.” No one has a perfect system anywhere!

Explaining the table

One thing you can notice from the table is that the early days were boring. As of the 20th day, the money wasn’t even up to $10,000. At that point, if you don’t understand the principle of compounding, you would have been angry for not taking the $1,000,000 option. But over the last 10 days, the money multiplied by more than 1000 times.

You see; patience pays because it takes time to grow wealth. As a matter of fact, time is one of the most important factors in compounding money, which is why it’s imperative that you start investing early to give your money time to grow. The growth at the later period is always astronomical. See the graph below:

The power of compound interest

So, you have seen the power of compounding in action. You could see how the penny compounded to over $5 million in 30 days, so it’s better to have a single penny that doubles every day for 30 days than take $1 million upfront.

Mathematically, you can calculate that with compounding formula:

A = P [1 + (rate)] ^ time

In this case:

  • P = 1 penny
  • Rate = 100%
  • Time = 29 days (because day 1 produced our P, so the compounding starts from day 2)

A = 1 [1 + (1)] ^29

A = 1 [2] ^29

A = 536, 870, 912 pennies = $5,368,709.12

As you can see, the main factors in compounding are the rate and the time. If the rate wasn’t 100% (doubling) or the compounding period and duration weren’t daily for 30 days, the money may not compound to that amount. For example, if the question was to increase the penny by 50% every day for 30 days, you would have only $1, 278.34. Or if it was to double the penny daily but for only 20 days, you would have $5,242.88.

Using the Rule of 72

Obviously, you can’t double your money every day when investing; no investment offers that kind of return. Most investments offer a single or low double-digit rate of return. So, you may want to know how long it will take to double your investment. You can do that with this simple method called the Rule of 72.

72 / Annual Return = Years to Double Initial Investment

You simply divide 72 by your annual rate of return on investment. That gives you the number of years it will take to double your initial investment

For example, if you invested $20,000 today at an 8% annual rate of return, it would take 9 years for that investment to be worth $40,000. It’s easy and interesting, right? The thing about investment is that at the early stages, it takes time to grow, but later on, it grows faster as the capital accumulates. In 27 years this investment would be worth about $160, 000. This is how wealth is built over your life.

The key lessons

The key lesson from this is that you should start investing early and often. Another one is to be patient with your investment: the biggest gains and returns always happen later in life. Make it a habit to invest a certain amount each year, even if it is in passive investments, such as mutual funds or ETFs.

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