FLASHCARDS: The Rule of 72 Explained: How Fast Will Your Money Grow?

🔎 Episode Overview

In this Flashcard Friday episode of Math! Science! History!, we’re diving into a simple yet powerful math trick: The Rule of 72. Have you ever wondered how long it takes for your investment to double? Or how quickly inflation can cut your purchasing power in half? The Rule of 72 offers a quick mental shortcut to estimate these changes without needing a calculator.

Join host Gabrielle Birchak as she breaks down the math behind this rule, explains why it works, and explores real-world applications in investing, savings, and inflation. Learn how small percentage changes can significantly impact your financial future, and discover why savvy investors use this rule to guide their decisions.

Whether you're new to finance or just love a good math hack, this episode is packed with valuable insights! Tune in, get smarter, and impress your friends with this easy mental math trick.

🧠 What You’ll Learn:

✔️ The Rule of 72 is a Quick Way to Estimate Doubling Time
✔️ It Works for Both Investments and Inflation
✔️ Could be a great party trick, if you’re feeling nerdy

🏛 Links & Resources:
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Episode Transcript

(00:00):
(Transcribed by TurboScribe.ai. Go Unlimited to remove this message.) It's Flashcard Friday here at Math Science History,
and today we're going to learn a math
trick.
Have you ever wondered how long it takes
for your invested money to double or disappear?
There's actually a math trick for that.
Hi, I'm Gabrielle Birchak.
I have a background in math, science, and
journalism, and today you're going to learn about
the rule of 72.

(00:23):
Let's set the scene.
Imagine you invest a chunk of money, say
$1,000, into an account that earns a
steady interest rate.
You know that compound interest is working for
you, but you don't want to pull out
a calculator every time to figure out how
fast your money grows.
Enter the rule of 72.
It's a simple formula that estimates how long

(00:44):
it takes for an investment to double, assuming
a fixed annual interest rate.
So here's how it works.
Take the number 72 and divide it by
your annual interest rate.
The result?
That's the approximate number of years it'll take
for your money to double.
For example, let's say your money is earning
an 8% annual return.

(01:05):
With that in mind, we divide 72 by
the value of the annual return, which is
8, and we get 9.
So, since you invested $1,000 at an
8% annual return, you should have about
$2,000 in about 9 years.
There you go.
It's simple mental math.
And note that I said 8 and not

(01:26):
8%, because if you were to divide 72
by 0.08, which is the equivalent to
8%, we would get 900 years, and nobody's
got time for that.
So why does it work?
Well, the number 72 comes from a logarithmic
formula for compound interest, where the precise doubling
time is calculated using natural logarithms.

(01:49):
However, for simplicity, 72 serves as a close
approximation, offering a quick way to estimate doubling
time for the most reasonable interest rates.
Now, let's talk about how to use it
in real life.
The rule of 72 is incredibly useful when
you're comparing different investments.
If a savings account gives you a measly

(02:10):
2% interest, we divide 72 by 2,
which gives us 36.
So, 36 years to double your investment with
2% interest.
Hmm, I wouldn't want that kind of an
investment, would you?
But let's say you decide to invest in
the stock market, which historically returns around 7
% per year.
Well, with that percentage, the doubling time is

(02:32):
much better.
So, we divide 72 by 7, and let's
make it easier.
Let's round down, which is 70 divided by
7.
This gives us 10 years.
You're going to double your investment in about
10 years.
This is why some investors often favor higher
return investments, like stocks, over low-interest savings
accounts.

(02:53):
If you leave your money in a high
-interest account or investment fund, you could see
multiple doublings over a lifetime.
Now, what about inflation?
Well, the rule of 72 isn't just for
investments.
It also works in reverse.
You can use it to estimate how quickly
inflation erodes your purchasing power.

(03:14):
So, say inflation is running at 6%
per year.
Using the rule of 72, we divide 72
by 6 and get 12.
That means in 12 years, the value of
your money will be cut in half.
During economic downturns, interest rates tend to drop
as central banks try to stimulate growth.
That means investments might grow more slowly, and

(03:36):
doubling your money could take longer.
For example, if an interest rate on an
investment fell to 3%, using the rule of
72, we find out that 72 divided by
3 is 24.
It would take 24 years for your money
to double.
So, as a quick note, the rule of
72 works best for interest rates between 6

(03:56):
% and 10%, where it stays within about
a 5% accuracy.
But if rates are lower, small adjustments can
improve accuracy.
I also want to point out that the
rule of 72 is just an approximation, not
an exact formula.
For example, at 2% interest, the rule
of 70 instead works for a better estimate.

(04:18):
At over 10% interest, the rule of
74 gives more precision.
For most people though, sticking with 72 is
good enough.
And if you really want to impress a
financial advisor, your accountant, your family, or even
your friends at a party, use the rule
of 72.
Because, you know, at a party, nothing says

(04:39):
a fun time like a smarty pants.
Okay, the rule of 72 is a powerful
reminder that time and interest work either for
you or against you.
Invest early to harness exponential growth, or risk
inflation and debt doubling faster than your savings.
So what can we take away from the

(04:59):
rule of 72?
Well, first, invest wisely.
Avoid high interest debt and hunker down to
keep up with inflation.
These are all critical for financial success.
Second, nothing in life is guaranteed.
Markets change, economies shift, and unexpected events happen.
Just like your health, your wealth needs regular

(05:20):
care, smart decisions, and a long-term mindset
to thrive.
You can do it.
I know you can.
Thank you for joining me on this Friday
episode of Flashcards.
That's all for today on math, science, history.
If you liked this episode, be sure to
subscribe and share.
And until next time, carpe diem!