A Penny Doubled For 30 Days vs. $1 Million Cash [Which Would You Pick?]

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It’s a common question:

Is it better to receive a smaller amount of money over a longer period of time, or a larger sum up front?

In this article, we’ll be approaching this question from a variety of perspectives in order to answer it once and for all. The answer may surprise you, so keep reading!

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One grain of rice and a chessboard

I’d like to start off this article with a fable.

Once upon a time, there was a very greedy king. For years, he had imposed a harsh rice tax on his subjects that had left many families hungry while his personal stockpiles grew larger and larger.

Now, the only thing that this king loved more than eating other people’s rice was chess. He played the game daily and was always on the hunt for new opponents.

One day, a man who was sympathetic of the people’s plight was visiting the king’s court. He decided to challenge the king to a game. To make things interesting, the king told him that if he won, he could have anything he asked for—and the man’s request was surprising.

Instead of asking for treasure, the man asked for rice. He told the king that if he won, he would return the following day to collect a single grain of rice. Every day after that, he would return for double the number of grains as the previous day. He told the king that this would continue for an entire month.

And the king thought to himself, the man asked for such a small thing, even though he could have asked for so much more. The king accepted this deal in a heartbeat.

Well, the man won—no surprises there. True to his word, the king had one grain of rice waiting for him on day one. Two on day two. Four on day three. Eight on day four. Sixteen on day five.

It wasn’t until the man arrived with a horse on the twentieth day to collect 1,048,576 grains of rice (around 149lbs) that it began to dawn on the king that he may have made a mistake.

Alright, let’s fast-forward to the thirtieth day. The man arrived at the palace gates with 70 horse-drawn carts to collect 536,870,912 grains of rice (around 76,695 lbs) which was redistributed to the hungry people.

To put that number in perspective, if you eat rice twice a day, every day for a whole year, you would only eat about 125lbs per year.

The moral of the story? Never underestimate the power of compounding interest. To drive that point home, let’s look at a thought experiment.

A penny doubled for 30 days? Or $1 million cash?

If you’ve ever played the lottery—or even seen a lottery advertisement—you may be familiar with the concept of lump sum payouts versus regular payouts. For those who aren’t, I’ll explain.

Lump Sum Payouts: A lump sum payout is—as the name suggests—a large sum of money that you get all at once. People love large sums of money, which is why most lotteries advertise lump sum jackpots.
Regular Interval Payouts: Regular interval payouts, on the other hand, are a series of payments made over time. If you were to win a regular payout, you would get smaller payments each day, month, or year for a set period of time.

Some lottery tickets offer either a lump sum payout or regular payouts. However, some tickets allow the winners to choose between the two payout options. That’s when things get interesting.

To illustrate why, imagine that you’ve just won the lottery—congratulations! I’m here to offer you your prize: either $1 million upfront or a penny doubled every day for 30 days.

Which do you choose? Let’s break down both of those choices.

$1 million cash

This is a simple one. $1 million upfront is exactly what it sounds like; you get a check for $1 million the day you claim your prize. We’ll ignore taxes for the sake of simplicity.

A penny doubled every day for 30 days – How much is that?

This option might not be as immediately appealing, but hear me out. On the first day, you get one penny. The next day, you get two pennies (double the previous day). The next day, you get four pennies (double the previous day), and so forth.

By the end of 30 days, how much would you have?

$0.01 × 2²⁹ = $5,368,709.12

That’s right, over $5 million. That’s an ROI of around 435% in a month. Surprisingly, choosing the doubling penny is far and away the better choice in this scenario.

Is it easy to double a penny every day for 30 days?

It’s quite easy to double a penny every day… up to a certain point. What is that certain point, you ask? Great question. The best way to lay this out is to write out how much doubling a penny each day is worth on each particular passing day.

Chart of doubling a penny every day for 30 days

Day 1: $0.01
Day 2: $0.02
Day 3: $0.04
Day 4: $0.08
Day 5: $0.16
Day 6: $0.32
Day 7: $0.64
Day 8: $1.28
Day 9: $2.56
Day 10: $5.12

Whew! 10 days passed and it isn’t looking too bad so far… let’s continue.

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

Ok! We just passed the $1,000 mark. Things are getting serious.

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

Now we’ve just passed the $100,000 mark. Things move extremely fast from here on.

Day 26: $335,544.32
Day 27: $671,088.64
Day 28: $1,342,177.28

A million bucks already? Alright, let’s just do the last two days for fun.

Day 29: $2,684,354.56
Day 30: $5,368,709.12

So as you can see here, it’s not easy at all to double a penny for 30 days. If it were, everybody would be a millionaire.

It varies from person to person, but I’d say starting at Day 19, when you’ve passed the $1,000 mark, it starts becoming very difficult to simply double the money for the rest of the month. If you did even a fraction of the month, you’d get to $100,000 in 7 more days, and to a million within a measly 3 more days on top of all that.

How much is a penny doubled for a year?

Just for fun, let’s calculate what a penny doubled every day for an entire year yields.

By the end of a year (365 days), how much would you have?

$0.01 x 2³⁶⁴ = 375 followed by 105 zeros.

There’s not even a name for that number. Let me just show you the number “quadrillion,” which is “a million billion” dollars:

$1,000,000,000,000,000

The result of our above calculation (375 followed by 105 zeros) is leaps and bounds beyond a quadrillion dollars, and enough money to last hundreds of generations easily.

The value of a penny doubled for a year is just completely insane and unfathomable to the human mind.

The power of compounding interest

So far, these stories and thought experiments have tried to drive home a simple point—compounding interest is a powerful thing. Now, it’s time to explain why in practical terms.

Most people think of money as having a static, parallel value (e.g., $100 equals $100). Most of the time, this is a perfectly reasonable assumption… but not always.

Things start to get weird when you add time and interest rates into the equation. If we take $100 at face value, it’s worth $100. However, if we think about the potential value of $100, it may actually be worth a lot more.

If you invest that $100 in a fund that nets you an average annual return of 7%, that $100 will become $762 in 30 years. So, is your $100 worth $100? $762? More? Less? Like I said, things get weird.

The concept I’ve outlined above is something Darren Hardy covers in his book The Compound Effect. While the concept is simple to understand, the implications are powerful. Let’s cover a few of them now.

If you invest the smart way, your money should double every seven year; even Einstein said so.

Think of money in terms of potential value

When it comes to saving money and weighing the pros and cons of a purchase, thinking about the potential value of your money can be incredibly helpful.

To illustrate, imagine you’re ordering something online. You start checking out and see that there are two shipping options:

Standard Shipping (Free): 5-7 days
Next Day Shipping ($3.99): 2 days

At face value, $3.99 might not seem like a lot for the convenience of receiving your order in 2 days. However, when you think about the potential value of the $3.99 it becomes harder to justify.

Again, let’s assume you invest that money into a fund that earns you a 7% annual return. After 30 years, your $3.99 will be worth around $30. Is 2-day shipping worth $30?

That’s for you to decide. However, thinking about money in this way can be helpful for putting purchases and savings into perspective.

How to get ahead by using compound interest – Invest early and often

The earlier you start investing, the more time your money has to grow. This is why Warren Buffett suggests that young people “start investing early and often.”

To illustrate, let’s say you have two friends—Jen and Rachel—who each want to retire with $1 million. Jen starts investing at age 25 and contributes $500 per month until age 65. Rachel doesn’t start investing until age 35 and contributes $750 per month until age 65. Both friends invest wisely and get a 7% annual return.

By the time Jen and Rachel, their investment portfolios have diverged quite a bit:

Jen’s Balance: $1,328,506 ($240,500 in principle)
Rachel’s Balance: $926,545 ($270,750 in principle)

That’s right, Jen contributed around $30,000 less overall and still ended up with over $400,000 more in the bank. Rachel doesn’t even manage to reach her goal of $1 million! How is that possible? Compounding interest.

The moral of the story is to start investing early and often. The earlier you start, the more time your money has to grow—and compounding interest will do the rest.

Retiring early using compounding interest

Compounding interest is how the booming FIRE community is making it work. Assuming a return of 4% per year, theoretically speaking you can take out that 4% the very next year and live off of that indefinitely. A whole lot of people are taking advantage of this and work hard for 10-15 years of their lives, save the money and retire way earlier than 65.

Learn more about the 4% rule here.

What kind of accounts have compounding interest?

Compounding interest is a concept that applies to various types of financial accounts. Here are some common types of accounts that typically offer compounding interest:

Savings Accounts: Many traditional savings accounts offer compounding interest. When you deposit money into a savings account, the interest earned on the principal amount is added to the account balance. Over time, the interest is calculated based on the new, higher balance, resulting in compounding interest growth.
Certificates of Deposit (CDs): CDs are fixed-term deposits with predetermined maturity dates. They often offer higher interest rates compared to regular savings accounts. CD interest can be compounded, meaning that the interest earned is reinvested back into the CD, leading to growth over the CD’s term.
Money Market Accounts: Money market accounts are similar to savings accounts but typically offer higher interest rates. Many money market accounts utilize compounding interest to help grow the account balance over time.
Retirement Accounts: Retirement accounts such as Individual Retirement Accounts (IRAs) and 401(k) plans can also have compounding interest. The contributions made to these accounts, along with any investment earnings, can compound over time, helping to build a larger retirement nest egg.
Investment Accounts: Some investment accounts, such as brokerage accounts or mutual funds, may also offer compounding growth. When you invest in stocks, bonds, or mutual funds that generate returns, the reinvestment of those returns can result in compounding growth.

Final thoughts

Compounding interest is a powerful force. It’s one of the most important concepts in personal finance, and it can help you reach your financial goals sooner than you think.

If you’re not already taking advantage of compounding interest, now is the time to start. Invest early and often, and let compounding interest work its magic.