The Miracle of Compound Interest

Compound interest is an amazing little thing.

It has been called the eight wonder of the world. There’s even a claim that Albert Einstein called it the most powerful force in the universe. I’m not sure if that’s true but it sounds cool on paper.

Whether he said it or not, compound interest is the most powerful force in investing.

It’s the hidden power behind why investing for the long term works so well.

What is Compound Interest?

In simple terms, compound interest is the interest you earn on your interest. When used in investing, the growth rate is more relevant. That may be confusing at first but let me show you an example to illustrate what I mean.

The above is a simple example that assumes you invest $10,000 in year one and leave it alone. The interest rate is set at 8%. Note that 8% is not a realistic “interest” rate when it comes to a bank account. When I talk about these bigger returns, I’m talking about numbers you can achieve via investments in stocks. More on that later. However, the concept still applies in a similar fashion although stock returns are going to be less consistent than a bank account.

You can see that in year one, you essentially make 8%($800/$10000) taking your total to $10,800.

Compound interest begins to work it’s magic in year two. The 8% interest is earned on the new total of $10,800 giving you $864 in interest. The next year, we see $933 in interest as you earn 8% on the prior year’s total of $11,664.

All of this happens without any additional investment. That’s the magic of compound interest. It’s interest on interest.

That means the starting point from which interest accrues is always increasing. It was $10,000 in year one giving you $800 in interest. By year 5, it was $13,605 due to the interest earned in prior years and that gives you $1,088 in interest.

The importance of time cannot be understated when it comes to compound interest. You can already see that you earn a lot more in year 5 than you do in year 1.

What happens if you extend it even further?

As time progresses, you get even more money! You can see that by year 30, your total has grown to over $100,000 and you’re getting nearly as much interest as your original investment.

That is the power of compound interest and why investing works so well.

What’s also obvious from this table is that time is on your side. The value of money in the account on year 30 is much higher than the value of that money in year 1. After year 30, your original investment is producing nearly $7,500 in interest, close to the total of your original investment.

One thing to remember is that interest rate plays a big factor here. Let’s take a look at the same table with 2% interest, something more realistic when it comes to bank accounts. These days even that number is high but rising rates may bring higher interest to bank accounts sooner than later.

The results are a lot less impressive. You can see that the 30 year total is far short of the total at 8% interest ($18,114 versus $100,627 at 8%). The reason for that is the lack of high interest payments. Since we’re earning interest on interest and the interest is a lot lower due to the rate, your end result is smaller.

Interest rate is really the driving force behind a higher total due to the magic of compound interest.

In simple terms, a low interest rate dulls the impact of the interest on your interest and your end result is much lower.

That’s why the long term rate is another key factor in long term investing.

If you’re investing $10,000 and getting a 2% return then your total after 30 years is just north of $18,000.

On the other hand, if you get an 8% return, your total is over $100,000. That’s a big difference!

The numbers get even higher as the rate goes up. You’ll notice I’ve changed the discussion from interest rate to rate of return and that’s key in this area as it really takes those bigger rates to build long term wealth.

For example, a 12% return will yield $300,000 after 30 years(including $32,100 in interest in year 30, 3x your original investment!).

A 15% return more than doubles that with $662,000 after 30 years(with $86,000 in interest alone in year 30).

Naturally, you’ll almost never get those rates of return from a simple bank account unless inflation is a long term problem. That’s where investing comes in because investing in stocks is key to achieving those higher rates of return.

Investors who can achieve a higher rate of return across many years will be richly rewarded due to the power of compound return.

That’s why people are so impressed with investors like Warren Buffet and why people seek investment returns above all else.

In his first 25 years at Berkshire Hathaway, Warren Buffet had a return of ~24% per year. That’s an insane return and if held across these same 30 years, would take your initial investment of $10,000 to nearly $6.4 million dollars.

It’s highly unlikely that anyone will be able to produce that type of return for that long a period anytime soon. However, it does serve as a good illustration to the power of interest rates combined with the compounding effect.

You can see how powerful interest on interest can really be when the long term return percentage is high. The difference between a 2% interest rate and something higher is huge.

Again, I’ve started using the term interest and return interchangeably. The reality is that interest(the rate of return you consistently get from a bank account) these days is just too low to achieve good growth. That’s why return becomes more important and return here is defined as the rate of growth that can be achieved from an investment.

What does that mean for you? It means that while time is on your side, a higher rate of return is very important as well. If you can find a safe interest rate of 8%, by all means take it, but for most of us, that’s just not possible. IBonds today in 2022 do offer that rate for a short period of time but that likely won’t last if inflation gets tamed.

That’s one of the reasons I and many others invest in the stock market for the long term. The stock market, unlike a savings account, has historically produced good long term returns. It is by far the best way to take advantage of the power of compound interest.

That doesn’t mean you shouldn’t keep any money in a savings account. It’s a safe place for low returns in the short term for money you may need in the next few years. Stocks, as seen lately, are volatile and while they can return 8%+ across a long period of time, in the short term, returns can be negative.

Still, for long term investing and growing your wealth, you need a bigger return than a savings account may offer.

That’s where long term investing using stocks comes into play. Let’s see how that works now.

Time is on Your Side – The First $100k is the Hardest

It’s nice to know how compound interest works in simple terms but I also want to take a look at it in action. When we talk about stocks, we’re not necessarily talking interest and we’re also not necessarily talking about consistency.

Here, we’re talking about rate of return which can vary any given year but has generally been in the 6%-10% range depending on your time frame. There are years when the stock market is down like right now and years where it’s up. However, the overall long term trend is up which makes the below work.

This return includes price appreciation from stocks as well as dividends paid out by certain companies.

The concept works the same way. Your initial dollars grow at a certain rate of return. Next year’s starting total is higher and your growth is now based on the higher number leading to a compounding effect. Naturally, the below is a perfect illustration of what can happen if the return is constant every year. With stocks, it will never be that smooth but conceptually it shows what I mean well.

Let’s imagine an investor who’s just starting out. Let’s call him Bob. Bob wants to fill his retirement safe with a barrel full of cash and he’s getting started now after growing his salary for a few years in his first job.

He’s read some books, done his research and wants to get started.  Bob has a plan in place, an asset allocation and wants to max out his 401k every single year.

He knows there will be some ups and downs but thinks he can get an average return of 8% by investing in a diversified stock account that meets his risk profile.

Our imaginary investor, Bob starts at $0 makes his first contribution of $18,500 in year 1 and another one on the first day of every other year for 25 years when he plans to retire. Where does Bob end up at the end of that period and how does that journey go?

The table above illustrates a similar concept we saw in the compound interest table. However, it adds a bit of complexity as contributions come into play as they often do with investments.

Bob still benefits from the compounding effect but also benefits from adding additional money every year.

He starts with $0 in year 1. He adds $18,500 each year and finishes with $1.46M after 25 years. That’s a pretty good result considering Bob’s contributions during that period were only $462,500. That’s a lot of growth!

What’s interesting about this table is how Bob gets there.

You can see that initially Bob’s contributions are the major source of growth. The first few years don’t benefit much from the compounding impact as Bob’s totals are rather lower.

However, that quickly begins to change as growth(our replacement for interest) becomes a bigger part of the overall picture. In fact by year 10, the 8% return on Bob’s portfolio begins to eclipse his annual contribution.

By year 15, the return portion is more than 2x the contribution and is the primary driver of portfolio growth. Near the end, Bob’s growth at 8% eclipses 100k and is nearly 6x more than his contributions. The contributions still matter but it’s compound growth that really drives the bus at that point.

The clear thing is that the impact of growth is bigger and bigger as the years go by.

I’ve often heard the comment that the first $100k(or the first million) are the hardest. The reason for that is that the compounding effect has little impact in those first few years. The growth on growth impact only becomes more apparent when the dollar totals are higher.

It takes Bob nearly 5 years to crest $100k. The next $100k comes before year 8.

In fact, once he’s at 300k, Bob is almost 50% of the way to million on a time basis. The reason for that is that the impact of compound growth is muted in the first few years as the growth is a small part of the overall picture. Once it starts taking off in the later years, so does the portfolio total.

It’s probably hard to visualize that so here’s the table above in a different format to help you see what I mean.

You can see that in this scenario, our imaginary saver Bob hits $1M right near the end of year 21.

What’s interesting is the path to that number. Like I said before, the first 100k is tough sledding since the growth part of the equation is small. It’s all contributions and that’s why it takes about 20% of the time to hit the first 100k. It’s 10% of the money but takes 20% of the time. You’re 24% into your journey time wise by the time you hit $117k.

Things start moving a bit faster after that but it still takes nearly 11 years to hit 300k.

That milestone happens between year 10 and 11 which means the first 300k happens right around the 50% time marker.

It’s right around then and especially after you hit 500k that the compounding effect really takes off.

Even if it takes a little while, compound interest eventually starts to pay off in a big way.

The growth is one of the reasons the rich get richer. The more money you have, the easier it is to make it work for you. However, it doesn’t mean that people starting at 0 can’t get there eventually either. Just look at Bob!

It takes some work and the journey can be slow and sometimes hard but the potential to make your money grow exists. It’s compound interest that makes it work.

In his 25 year journey, Bob ends up contributing $462,500 and ends at 1.46M. That’s the power of growth, contributions and compound interest.

Even if you can’t contribute as much as Bob, your money will still grow for you. It might take longer to reach a million but it’s possible.

If you’re lucky to contribute more then the path will be faster and you’ll be a millionaire sooner.

It’s important to remember one thing that we talked about earlier.

The rate of return(interest rate) does matter a lot. 8% will never come risk free and it can entail some difficult times when the stock market drops like it has recently. However, the long term trend is up and these tables show how it’s possible to become a millionaire through diligent saving and the benefits of compound growth.

You can use a website like this one to see how the S&P 500 has done in various time periods. It’s hard to predict exactly where stocks will go in the future but stocks have generally brought in 6-10% depending on the time frame you’re considering. Even someone who put money in on January 1 2008, right before the market crashed 38% that year still has a 9%+ annual return even after this year’s correction. That’s a pretty good return considering what’s happened recently and in 2008.

It does take some time. However, a lot of the work is done for you through compounding. It takes 21 years to get to $1M with the above contributions at 8%. Most of that money comes from growth as contributions only make up $388,500 during this 21 year period.

If you’re lucky and maintain a higher rate then $1M will come even faster. If you’re a bit more conservative then it’ll take a bit longer. Even at 6%, an investor would reach $1M after 25 years – not as good but still a reasonable timeline for standard retirement.

The reality is that growth matters a lot. This type of portfolio expansion wouldn’t be possible without a relatively high return. At 2%, it would take over 37 years to reach $1M and most of that money(684k) would be from contributions and not growth.

That’s why the stock market is the way to go for most people. It’s the only proven way to find those types of returns in the long run. It can be stressful as there will be years where you lose 20%+ of your money but the long term trend is favorable as long as you can stomach and keep buying during those years.

Compound interest eventually pays off in a big way. It might not seem like it at first. Those first few years may drag but even in small amounts, it’s making a difference. It definitely feels like you’re running uphill at first until you reach a certain point where the compound effect is more visible.

None of this can happen on its own. It does need a kick start from the investor to get things going.

The path to $1M above will never happen if Bob the investor doesn’t start with $18,500 on day one. It takes much longer if he doesn’t contribute $18,500 consistently every single year. It doesn’t work if Bob panics and sells when the market drops. This only works if Bob keeps investing and holds on through thick and thin.

It’s a long term game but compound interest is on your side. Investments can go up, they can go down but it’s important to keep things in perspective. It took Bob 21 years to get to $1M, it’s not a sprint, it’s a marathon.

Time in the market matters and it’s all because of the miracle of compound interest.