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Teaching children about the power of saving and investing can sometimes be a challenge, especially for young minds.
With a bit of creativity and a compelling story, you can turn this important life lesson into an adventure.
What's worth more - a million dollars today, or a penny that doubles every day for 30 days?
In this article, we explore the popular question of doubling a penny vs a lump sum.
We'll illustrate the surprising answer through an enchanting tale of two pirates.
Are you ready to dive in?
Let's dive straight into it: what's worth more - a million dollars today, or a penny that doubles every day for 30 days?
The answer is quite surprising.
That single penny, when doubled every day, greatly surpasses the one million dollars.
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!
Yes, you read that right.
More than five million dollars from just one penny.
By day 30, it grows into an astonishing $10,737,418.24!
It's all thanks to a financial phenomenon known as compound interest.
Through compound interest and growth, small amounts can turn into a fortune over time.
This process is similar to what happens when we invest money and let it grow.
In many ways, this is how generational wealth is built.
give it time, and it starts growing at an alarming rate
The growth might seem slow at first, but give it time. After the beginning it starts growing at an alarming rate, much like a snowball rolling downhill.
Meet Jack and Isabella, two adventurous pirates sailing the seven seas.
They're on a thrilling quest to find the long-lost treasure of the legendary Captain Taylor.
One day, their map leads them to an uncharted island. That's where they uncover an ancient chest buried beneath a gigantic palm tree.
Inside the chest, they don't find piles of gold or strings of pearls.
Instead, they find a small, weathered gold coin and a note in Captain Taylor's handwriting.
The note gives them each a choice: they can take a ship filled with a million gold coins waiting for them at the island's shore.
Or, they can keep this single, magic coin that will double in value every day for a month.
Jack, eager for wealth, chooses the ship full of gold coins, leaving Isabella with the single gold coin.
He dreams of all the trinkets and treasures he could buy with a million gold coins.
Isabella places the coin in her tiny piggy bank that she carries on all her adventures, a gift from her grandmother.
The first few days were humble beginnings for Isabella.
On day 4, she has 8 coins jingling in her piggy bank.
By day 6, she has 32 coins - and her piggy bank is full!
She realizes she'll need better storage solutions for her growing fortune.
On day 10, she has 512 coins, enough to fill a treasure chest.
It's a big increase, but still nowhere near Jack's fortune.
By day 16, with 32,768 coins, she fills up a room with treasure chests filled with coins.
Isabella's fortune keeps growing.
On the 21st day, Isabella's fortune surpassed Jack's with 1,048,576 coins.
Her ship is no longer enough.
On the 30th day after getting her coin, Isabella's magic coin has turned into a mind-boggling 1,073,741,824 coins.
She has to buy a massive castle just to store her treasure!
Jack is amazed.
He thought he had made the wise choice, taking the million coins upfront.
But he watched as Isabella's single coin outgrew his million, all because of the magical power of exponential growth.
The pirates learned a valuable lesson that day.
They learned about patience, growth, and how small savings can grow into a fortune, thanks to the magic of compound interest.
The power of exponential growth becomes clearer when we look at the daily growth of a single penny over 30 days.
Notice how the growth is relatively slow at first, but from Day 20 onwards, the amount starts skyrocketing
Here's how it unfolds:
Notice how the growth is relatively slow at first, but from Day 20 onwards, the amount starts skyrocketing.
On Day 27, it passes the one million dollars mark and continues to grow fast.
One thing to pay attention to is that starting with Day 0 ensures we don’t miss that critical first day.
On the 29th day that it doubles, the penny grows to $5,368,709.12
It’s easy to think of Day 1 as the beginning, but if we do that, we would inadvertently skip the first doubling.
By beginning with Day 0 at $0.01, we correctly account for all 30 doublings, demonstrating the full exponential growth that occurs over the course of 30 days.
This isn't just a cool math trick or a fun story.
Exponential growth is real-life magic that works in the world of investing.
Exponential growth is real-life magic that works in the world of investing.
Let's take an example from the real world.
In this scenario, the parents set up a financial gifting page for their baby. They receive financial gifts from friends and family.
They decide to invest the $1,000 they received as gifts when the child is born for the long term.
With an average return of 10% per year, by the time the child turns 21, the initial investment would have grown to approximately $8,095.
If you left the investment untouched until the time the child reaches 70 that $1,000 investment would have grown to approximately $1,065,281
And what if you kept that investment going?
If left untouched, by the time the child turns 35, the original $1,000 investment would be worth around $32,638!
If you left the investment untouched until the time the child reaches 70 - a typical retirement age - that $1,000 investment would have grown to approximately $1,065,281.
This dramatic growth over time showcases the magic of compound interest and the importance of starting to invest early.
As parents, you can tap into this magic to help secure your child's future by investing for your kids.
Set up financial gifting for your kids.
Invest with tools like 529 plans for education, IRAs for retirement, or UTMA accounts for general use.
If you start with 1 penny and double it every day for 30 days, you would have approximately $10,737,418.24.
This calculation assumes perfect doubling each day.
This is not typically possible in real-world investing, like investing in the stock market.
But, it shows the power of exponential growth.
Doubling a penny every day for 365 days results in a number so large that it is hard to understand.
If you double a penny every day for 365 days, you're essentially performing the operation 2^365 / 100. That's 2 to the power of 365. Then divide by 100 to get dollar amount.
This results in an un-imaginable amount that is 1 followed by 107 zeroes.
This is far more than all the money in the world.
It shows the power of exponential growth, but also highlights that such growth rates are not sustainable in the real world.
If you start with 1 dollar and double it every day for 30 days, you would have approximately $1,073,741,824.
This shows the concept of exponential growth.
Like the penny example, this is not typically possible in real-world investing scenarios.
The real-world lesson here is the importance of investing regularly and the power of compound interest over time.
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