A Penny That Doubles Each Day for a Month vs. $1 Million
If you were given the choice between a penny that doubles everyday for a month or a lump sum of $1 million, which would you choose? If you’re familiar with the “Would You Rather” questions, you know the answer isn’t as straightforward as it appears.
On the surface, $1 million seems like the obvious choice. It’s an easy decision because who wouldn’t want a million dollars? But if you carefully consider the two options, the penny that doubles everyday for a month may be the better option.
How? Let’s take a closer look at the math behind this question to help you understand the potential outcomes of each option. Don’t let the math scare you off, we promise to keep it simple and clear.
How Much Is a Penny Doubled Everyday for 30 Days?
If you had a penny that doubled every day for a month, you would have about $5,368,709.12 on the thirtieth day. That’s because your money is doubling daily. In other words, you would have five times more money than if you had opted for the $1 million upfront.
On the other hand, if you took the $1 million offer, you would still have the same amount at the end of the month. In this case, it would be more beneficial to have the penny that doubles each day for a month, as the final amount would be significantly more than $1 million.
The Chart of a Penny Doubled for 30 Days
As you have seen, if you double a penny for 30 days, you’ll have more than $5 million. But how did we get the $5M+? Here’s the math:
What Is the Lesson Behind the Penny Doubled for 30 Days Question?
The penny doubled for 30 days vs the $1 million question teaches a valuable financial lesson. Doubling money and time go hand in hand. If you look at the penny doubled for the 30 days chart above, you’ll notice how important the 30 days time frame is and how your choice would change if the number of days were reduced.
Here are a few observations:
- The penny did not reach $100 until the fifteenth day.
- The doubling penny was still less than $1 million on the 27th day.
- It took the 28th day to reach and surpass the $1 million mark.
Investing early is key because growing wealth from your savings takes time. You will reap the greatest benefits if you invest early and allow your money to grow. That’s why it’s always a good idea to start saving for retirement as soon as you start working.
If you were to choose between $1 million and a penny doubling for 27 days or less, going for the $1 million would make sense. It may take some time before you see any results, so investing requires you to have a long-term goal in mind.
Double a Penny for 30 Days in Real Life
You’re unlikely to find an investment that doubles your money every day, but you get the point. It all comes down to understanding how your money grows so that you can make the best decisions to maximize your returns. In short, timing is crucial in taking advantage of the power of doubling.
In real markets, it can take years to double your money, not a month. How long will it take to double your money if you invest in the stock market, for example?
We have a simple formula that will help you understand how long it will take for your invested money to double in value: the Rule of 72. It works with compounded interest rates and gives the most accurate estimates for interest rates in the 6% and 10% range. So let’s first understand compound interest.
What Is Compound Interest?
Before we get to the Rule of 72, it’s good to be familiar with compound interest. Knowing how your money grows is essential to help you maximize your returns. Your money can grow through either simple or compound interest.
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. It is the effect of “earning interest on your interest,” which can grow a sum of money faster than simple interest, which is interest calculated only on the principal amount.
For example, if you put $200 in an investment vehicle with an 8% annual interest rate and compound interest is paid annually, at the end of the first year, you will have earned $16 in interest. If the interest is compounded annually, the following year’s interest will be calculated on the initial principal of $200 and the $16 in interest accumulated in the first year, resulting in an interest payment of $17.28. And the cycle continues. As the interest compounds over time, the amount of interest earned each year will increase, resulting in a faster growth rate for the initial principal.
The frequency of compound interest can vary, with some accounts compounding daily, monthly, quarterly, or annually. The more frequently the interest is compounded, the faster the money will grow.
The Rule of 72
The Rule of 72 is a quick and easy way to estimate the years it will take for an investment to double in value, given a fixed annual interest rate. To use the Rule of 72, divide 72 by the interest rate.
The number of years to double your money = 72 / annual return.
The resulting number is the approximate number of years it will take for the investment to double. For example, if you have an investment earning a 9% annual rate of return, it will take approximately eight years for the investment to double in value (72 / 9 = 8).
The Rule of 72 is a rough approximation. The exact number of years it’ll take for your investment to double in value can differ due to various factors. However, it is a useful tool for quickly estimating the time it will take for an investment to grow, especially when comparing different investment options with varying interest rates. This can help you make an informed decision about which investment may be the most suitable for your needs and goals.
Here are a few examples of how the Rule of 72 works:
- At a 4% annual rate of return, it will take approximately 18 years for an investment to double in value (72 / 4 = 18).
- At a 6% annual rate of return, it will take approximately 12 years for an investment to double in value (72 / 6 = 12).
- At a 10% annual rate of return, it will take approximately 7.2 years for an investment to double in value (72 / 10 = 7.2).
The penny doubled for 30 days vs. the $1 million upfront question teaches us one of the most valuable investing lessons. Invest early and often with a long-term goal in mind. It takes time to build wealth with your investments, and it may take some time to see the desired results. The longer you’re invested, the better the returns.