Will An Index Fund Make You Rich? The Maths Behind The Magic6 min read

When it comes to investing, there is a common misconception that you need to pick winning stocks to become rich. In fact, the opposite is true.

As I recently explained in my post busting the 9 biggest myths in investing, the best indicator of long term investing success is time. In this post, I’ll demonstrate why.

As we know, index funds work by tracking the performance of an index. This means that investing in an index fund is exactly the same as betting that an index will perform well. Therefore, the question for us becomes: do we think that the value of a diversified index will increase over time?

To give you a real world example, let’s use the results of the S&P 500 Index.¹Note that this table isn’t 100% accurate, as it excludes income received from dividends.We’ll also assume that the S&P 500 is ‘diversified enough’. The battle rages on as to whether it is too US-centric, but I’ll address that at a later date. The chart below shows the year on year returns since 1951.

As you can see, in 1954, the S&P 500 index grew by a whopping 45%. This means that if you’d invested £1,000 in an index fund tracking the S&P 500 Index on 1st January 1951, by the end of the year you would have £1,450. Congratulations. You just made £450 by holding the fund for a year.

This is a phenomenal amount of growth when compared to the 1% per annum interest you can expect from a top rate savings account today. Not too shabby when you consider you barely had to lift a finger, eh?

Great, so it’s that simple? I can invest today and make 45% every year?

Well, not quite.

Let’s choose a different year. Take a look at the results for 2008. If you’d invested £1,000 on 1 January 2008, then by the end of the year your investment would be worth … £620. That’s right. You just lost £380. Now that’s not as much fun, is it?

This pattern of randomness has occurred since the S&P 500 Index was first created. If you examine the table above, you can see that performance year on year fluctuates massively.

Just look at the period between 1973 and 1977. Down 17.4%, down 29.7%, up 31.5%, up 19.1%, down 11.5%. It’s a white knuckle rollercoaster of financial performance, and it never slows down.

Right. So some years are good, and some years are bad. How do we pick the winners and avoid the losers?

You’d be forgiven for thinking that you need a crystal ball to make money with an index fund. How do you know if the fund will perform well in the year that you need it to? Well, put simply, you don’t know. But then again, you don’t need to.

Instead of picking winners or losers, you can use the one secret weapon in your arsenal which is near enough guaranteed to produce results. And that weapon is none other than time itself.

Good years or bad years, fun times or sad, we let Father Time take care of everything.

How does this work in practice? Well, since the inception of the Composite Index in 1923 (which later became the S&P 500 Index), the index has delivered an average annualised return of 10.59%.

Adjusted for inflation, this is equal to a real return of 7.49% per year. This means that, on average, your money will grow by 7.49% per year over the long run.

And the longer you hold the fund, the more chance you have of riding out any short term volatility in performance.

The following table illustrates this concept nicely. It shows the best and worst returns that the S&P 500 Index has produced for a variety of time periods.

As you can see, the worst return that the S&P 500 Index provided over a 15 year period was 4.3% per year. That’s still way higher than what you can expect from a standard savings account.

And that’s just the worst case scenario. The best 15 year period in the history of the S&P 500 Index returned 18.9% per year. That’s the stuff dreams are made of.

The bottom line is this: as long as your investment is diversified enough, then the longer you hold it for, the greater your probability of gains in the long run.

So my parents were right. Patience really is a virtue. But what sort of money will this actually make me?

The real power of investing is revealed when we introduce your second secret weapon: compound interest.

The concept of compound interest is simple. It’s interest that you earn on your interest. Progress on your progress. Gains or your gains. Let’s look at an example.

If you tuck £1,000 away into an index fund which gives you a return of 10% every year, after one year you will gain £100. You now have £1,100.

The year after that however, you’ll gain 10% on £1,100. This gives you £1,210. The year after that, 10% of £1,210. Now you have £1,331. And so on, so forth.

The increases you receive every year are growing because you’re earning profit on top of your profit. And these increases keep on getting larger with time.

Once the effects of compounding interest really kick in, it can be rocket fuel for your investments. Don’t believe me? Check this out.

If you’d put £100 in an index fund which tracked the S&P 500 Index since its inception in 1923,²It was called the Composite Index at this time. that £100 would now be worth roughly £3,413,505 before inflation.

That’s right, over three million pounds in today’s money. Not bad for a £100 investment now is it?

That is an eye-watering amount of cash. Do you have a time machine so I can hop back to 1923?

Unfortunately, unless you’re Captain America, you weren’t alive in 1923. But to get the benefits of compound investing, you don’t need to be.

Let’s assume you invest £500 every month in an S&P 500 index fund at the inflation adjusted rate of 7.49% per year. In just 15 years, your investment would snowball into £167,975.79.

Don’t fancy stopping after 15 years? Let’s try 30. You now have £681,268.91.

But what about if you push yourself and save an additional £500 every month, taking your total to £1,000 invested in the fund each month? After 30 years, you will be the proud owner of a cool £1,362,537.83. And over £1,000,000 of that will have been earned in interest alone!

Break out the champagne. I’m going to be a millionaire!

You definitely could be. But remember the fundamentals.

Time is the key factor in all of this. The more you save, the sooner you buy, and the longer you hold for, the greater your chances of riding out the bumps and making a shed load of profit down the line.

I should also point out that while an S&P 500 index fund is the chosen investment for many people, it isn’t the only index fund out there.

Some people actually argue that the S&P 500 Index isn’t diversified enough because it is overly reliant on the US economy. These people prefer to invest in larger and more diversified index funds, such as a Total World or Global Cap Index Fund, which covers the entire global economy.

But more on that at a later date.

For now, you can treat yourself. Because you’ve just learnt one of the most important lessons you can ever learn about investing: compound interest over time is one of the easiest paths to wealth.

For tips on how to save your hard earned cash so that you have more to invest today, read my posts on the fundamentals of being frugal and why tiny everyday gains matter.

I’ll see you in the next one.

Note: As usual, I sprinkled some external links to other articles throughout the post in case you want to read more about any of the concepts mentioned above. I try to make my posts easy to read and understandable, but sometimes seeing something explained in a different way can be helpful too!

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