Why Compound Interest is the 8th Wonder of the World
“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”
It may seem that our genius friend Albert here was exaggerating a bit, but the math checks out. Believe me— I was insane enough to earn a degree in Math.
Still, you don’t have to be a genius or a math major to understand the power of compound interest, or put more simply, the interest you earn on interest when investing.
The formula below is read as: Future Value equals the principal times one plus the rate of growth to the power of the number of years you are invested.
Compound Interest Formula:
FV= P x (1 + r)^n
There are 3 main inputs into the compound interest formula to determine the future value (FV) of your account.
The P stands for principle— this is the amount you start with in an account,
the “r” stands for the annual return as a percent,
and the “n” stands for the number of years you invest.
The carrot (“^”) up top denotes an exponent— meaning you multiple (1+r) together “n” many times. For example: If you put $1,000 in a savings account with a 5% return, in 5 years you will have: 1000*(1+0.05)^5= 1000x(1.05)x(1.05)x(1.05)x(1.05)x(1.05)=$1276.
Takeaway: $1,000 can turn into $1,276 in five years when you earn just 5% a year.
Voila! $1000 turned into $1276 over 5 years while you slept. Not too shabby. But still, it doesn’t really scream “8th Wonder of the World”. So, let’s change some of those variables to see how our fortune changes in response.
What if we changed the “r” and earned 10% a year?
This is not outside the realm of possibility— U.S. stocks have averaged about 10% annually for the last 40 years. Our $1000 in 5 years would become $1,610, which is quite a bit better than $1276. Again, not too shabby. But we can still do better.
What if we changed the “n” and instead we stayed invested for 10 years instead of 5 years? The original $1000 becomes $2,594. Okay, now we’re talking.
(Note that the $2,594 figure is not adjusted for inflation).
Now here is an example of a civilization that could hold on for the long-term.
Last time when I doubled the interest rate, there was a slight improvement, but when we doubled the time, the result was multiple times better.
It appears that the time spent invested is a very powerful factor in this equation.
Check out how the $1000 grows over 40 years, assuming 10% annual interest:
After 40 years, the balance is $45,255.
That’s a lot more impressive! Often, this typical compound interest example stops at 40 years of compounding because 40 years is about the timeframe someone might have from age 25 (when they might have a job and begin to save) to age 65 (when people want to think about retiring).
This is why every personal finance article on the internet and your Uncle Bill gives out the financial advice: “start early!”
Uncle Bill’s desk from 1979. Canva needs to update their stock photo choices.
And the numbers start to get really mind boggling when you stretch out to 60 years, when the initial $1,000 turns into over $300,000!
Imagine if you put aside $1,000 today for your kid’s retirement??
My advice, which is a bit of a twist on the “start early” refrain, is to think about your spending in light of the opportunity to invest the money instead.
“For every dollar you spend today, you are giving up the opportunity to spend some multiple of that dollar in the future.”
I believe saving shouldn’t be an end in itself— you should eventually reap the benefits of the delayed gratification and be able to spend that money, baby!
Even when adjusting for the impact of inflation (assuming prices rise 3% annually and sticking with our 10% annual return example)…
…If you don’t spend and instead invest $1 today, you can spend $2 in 10 years. Or the $1 becomes $4 of spending power in 21 years.
Lastly, to circle back to Mr. Einstein’s quote— we’ve seen that compound interest is so powerful for savers. That same power works against you as a borrower.
What if you borrowed $1,000 today on a credit card with 20% interest and didn’t pay it back right away? The chart below shows your true cost when making minimum payments.
If you made it this far, thanks for sticking with me through all that boring math. Now get out there and use your newfound compound interest powers for good! ~Stacy
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Inspired man about to crush his credit card debt and embrace the 8th Wonder of the World.
About the Author:
Stacy Dervin, CFA, CFP® provides fee-only financial planning and investment management services in Eugene, Oregon. Tailored Financial Planning (TFP) serves clients as a fiduciary and never earns a commission of any kind. As a financial advisor, Stacy is on a mission to help Gen X and Gen Y be truly proactive about their financial futures.
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