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Albert Einstein is widely reported as having made the statement, “The most powerful force in the universe is compound interest,” and after looking at the math behind this concept, I definitely agree with him.

## Definition

Wikipedia defined the concept of compound interest as elegantly as I’ve seen: “Compound interest arises when interest is added to the principal of a deposit or loan, so that, from that moment on, the interest that has been added also earns interest. This addition of interest to the principal is called *compounding*.”

I know a lot of people can get lost with detailed mathematical formulas, so we’ll skip those, but this is so unbelievably important to understand and appreciate that we need to run an example.

## An Example

Let’s say you deposit $10,000 into an account that pays 10% interest and it compounds once annually. At the end of the first year you have your original $10,000 plus the $1,000 interest you earned ($10,000 x 10% = $1,000) for a total of $11,000.

At the end of the second year you’ve earned $1,100 in interest ($11,000 x 10% = $1,100), which is added to your $11,000 balance for a total of $12,100.

If compounding didn’t exist and you were only paid the 10% interest on your initial deposit, you’d have a total of $12,000 (your original $10,000 plus $1,000 interest paid at the end of Year 1 and another $1,000 paid at the end of Year 2).

This $100 difference doesn’t sound like much, right? How can this be “the most powerful force in the universe” or a “miracle” as it is often called?

Let’s look at this example at different intervals over a 100-year period:

**Just for fun though, first try to guess how much the final balance will be in the compounded example at the end of Year 100 and let me know what your guess was in the comments section below **(as a little inspiration, you know the non-compounded number will be $110,000 (100 years of $1,000 interest pus $10,000 initial investment)):

At the end of Year 10 we’re up to a $5,937 difference, which is a large number, but still not life-changing.

By Year 25 we’re already almost up to the full $110,000 you would have in the ‘no compounding’ example **at Year 100**.

At the end of Year 30 the difference has ballooned to $134,494. The ‘no compounding’ example has $40,000 as you would expect (30 years of $1,000 interest plus the original $10,000), but the compounded version has $174,494!

By the end of Year 50 the difference is up to $1,113,909 and amazingly by the end of Year 100 the compound interest example has a balance of **$137,806,123** compared to only $110,000 in the non-compounded version. Yes, that is **$137.8 MILLION dollars**! It’s not a typo or a joke — that’s just the math.

Now you can see why everyone who understands this concept is so blown away by it!

The most important take away from this example is that compounding matters and the length of time matters, so you need to allow this miracle of compounding as much time as possible to work its magic. Invest as early in life as you possibly can with as much money as you possibly can!

Let’s look at the compounding example but with “only” an 8% interest rate:

Again, the difference isn’t that large after Year 10, but let’s look out to Year 100:

While the difference between the 10% and 8% rates doesn’t sound enormous in theory, you would have $115,808,510 less at the end of Year 100 in the 8% example (or only 15.96% of the total balance)!

What that means to me is that every little bit of additional return on your investment is essential, and you have to do everything in your power to maximize your return.

As we’ll show in a follow up post, since there basically isn’t a person alive who can beat the stock market returns over a 50 or 100 year period, the best way possible to do this is to invest in an ultra-low expense ratio mutual fund that mirrors the total U.S. stock market.

Charles@Gettingarichlife.com says

Hi Brad

I saw your article in 1500 days blog. I’m a blogger from Hawaii and I read that is one fo your favorite states to visit. Building wealth in an expensive state is very difficult, I wish we had your cost of living. I agree with your compound interest, i actually wrote about this Einstein quote in a post. It’e great thst you are trying to help others in spreading the personal finance knowledge. Hope to see you around.

Brad says

Charles,

Thanks for stopping by and commenting! I’ve always been astounded by the concept of compound interest, but never more so than after writing this article. Glad you enjoyed it!

Andrew@LivingRichCheaply says

Great post! Everybody likes to say they know the power of compounding but it makes a difference when you actually see the numbers. I was talking to a friend recently who had yet to invest at age 30. He said that once he earns a larger income, he’ll start saving and investing in large amounts. Well, with the power of compounding…time matters…so even investing a little bit will make a difference. I’ve been investing for about 10 years and it’s not until around this time that you REALLY see the power of compounding. It can be frustrating in the early years but you just have to be patient.

Andrew@LivingRichCheaply recently posted…Patience is a Virtue

Brad says

It’s sad when people say, “I’ll invest someday…”, because we all know that something will always come up and that 30 year old will wake up and be 60 and have no clue why he has no money saved up. It’s so easy to spend, but it’s not so easy to be smart and actually save.

You’re absolutely right about being patient — the more years you have to compound, the better. That’s really why I try to think on a 50-year time horizon and hope that we can make our children and grandchildren rich someday.

Abin says

Hi Brad:

What would be a good place to invest where compound interest is used extensively?

Kyle | Rather-Be-Shopping.com says

Wow, those numbers are staggering. It goes to show that you just need TIME…I always tell folks that NOW is the time to start investing in a Roth IRA – don’t wait!

Kyle | Rather-Be-Shopping.com recently posted…Retailer’s Big Secret: Crack the Price Tag Code

Brad says

NOW is always the time — you’re absolutely right! Especially with a Roth-IRA, you can start as soon as you have “earned income.” Putting money away when you’re a 19-year old with a summer job isn’t the first thing on your mind, but if that kid has smart parents, they can contribute to the Roth for their son/daughter, and that money easily has 40-50 years to compound before they’ll need it!

Pretired Nick says

I do loves me up some compound interest! Great post, buddy!

Pretired Nick recently posted…Guest Post: The Awesome Magic of Investing Like An 8 Year Old

Brad says

Thanks Nick — glad you enjoyed it! It truly is a remarkable thing to see it on the screen like that…

Done by Forty says

Here’s the one area where traditional retirees have a big advantage over early retirees. As they’re more likely to let compound interest work its magic for longer periods of time (presuming they start early), they get way more benefit from this miracle than an early retiree typically would (as they’re most likely going to start drawing down on their nest egg right out of the gate).

It’s crazy to see the impact of even a 2% delta in annual returns compounded over time. That speaks to certainly finding the best returns but also (and perhaps more importantly) finding funds that don’t charge 1-2% more in fees.

Done by Forty recently posted…How Should FIRE Timeline Affect Asset Allocation?

Brad says

You couldn’t be more correct both about the traditional/early retiree scenario and most importantly the impact mutual fund and advisory fees have on your ultimate return.

I still can’t believe the 8% return scenario only produced such a tiny fraction of the ending balance as compared with the 10% return scenario. If that doesn’t speak to the power of using a total market index mutual fund for essentially all of your long-term investing, I don’t know what will.

There’s simply no way you, me or anyone else can beat the market over a 50-year period, so why not own the returns of the entire market for just about zero cost (.05 expense ratio in Vanguard’s Admiral class U.S. Total Stock Market Index Fund (VTSAX))?

EB says

I guessed 3 million – that’s amazing!

Brad says

Thanks for guessing — that’s actually one of the higher ones I’ve heard!! Isn’t it just remarkable?? Ours brains just aren’t equipped to handle the enormity of this concept, which makes these guesses so interesting…