The Miracle Of Compound Returns

Those who understand compound interest are destined to collect it.
Those who don’t are doomed to pay it.

So, what is compound interest?

Albert Einstein, well known for being smarter than the average bear, once called compound interest “the greatest mathematical discovery of all time”. But you don’t need to be as intelligent as Einstein to understand compound interest. In fact, it is a very simple concept.

The concept is this. When you invest money you earn interest on your capital. The next year you earn interest on both your original capital and the interest from the first year. In the third year you earn interest on your capital and the first two years’ interest. You get the picture. The concept of earning interest on your interest is the miracle of compounding.

It’s very much like a snowball effect. As your capital rolls down the hill it becomes bigger and bigger. Even if you start with a small snowball, given enough time, you can end up with an extremely large snowball indeed.

Here at the Fool, we like the concept of compound interest so much, we came up with the five Foolish Laws of Compounding.

1. Start Early Fool!

The earlier you start investing, the more time you leave for the miracle of compound interest to take effect. Someone who invests £100 a month from age 20 to 29 and then lets their investments grow is likely to have more money at 60 than someone who invests £100 a month from age 30 to 59.

2. Small differences in return matter. A lot!

Over long periods of time, the difference between investing at, say, 7% and 8% is enormous. If you don’t believe us, try experimenting with the calculators above.

3. Don’t squander your inheritance on sex, drugs and rock’n’roll. (Unless you want to, that is)

Investing isn’t everything. Like most things in life it is best to strike a balance. With investing it is the balance between enjoying yourself now and providing for your future.

4. Over time, regular saving of quite small amounts can build up an astonishing sum of money.

If you save £100 a month for 40 years and your investments compound at 12% a year how much will you have? The answer is an astonishing £980,000!

5. Time and patience are the friends of compounding and, therefore, of investing.

Saving for 40 years is obviously something you can’t do overnight. You have to exercise patience if you want to feel the full benefit of compounding.

The Rule of 72

Although this part of the site has some calculators to help you work out the effects of compound interest there is also a handy shortcut known as the Rule of 72. It states that you can find out how many years it will take for your investment to double by dividing 72 by the percentage rate of growth. So it will take 9 years for your investments to double if they grow at 8% a year (72/8=9). But it will only take 6 years if your investments grow at 12% and so on. The Rule of 72 only provides an approximate answer but it is sufficiently accurate for many calculations.

We have two calculators to help you work out:

However, there are a number of points to note. First of all neither calculator takes taxation into account. As everyone has a different tax situation and the tax regime alters over time, it would be hard to model this into the calculator. If you invest in an ISA then your investments have the opportunity to grow free from tax. You also get tax-protection in a pension plan but, currently, you are taxed on your pension when you start to draw from it.

What rate of return should you use?

There’s no correct figure to use — the future is unknowable after all — but it’s important to be realistic about the rate of return you expect from your investments.

Historical returns can give you a steer. Since 1869, the UK stock market has returned an average of around 9% a year. However, returns over shorter periods have been much more variable. For example, average annual 20-year returns during this period have varied from as low as 3% to as high as 20%. Even over 50-year periods, returns have varied from around 5% to 14%.

And don’t forget you need to consider the costs of investing, too. In a plain-vanilla index tracker these could be as little as 0.25% a year. In other types of investments, charges could knock 1%-2%, or even more, off your annual returns.

What about inflation?

The stock market returns quoted above are what is known as the nominal rate. Adjusting for the effects of inflation, the average annual real rate of return since 1869 has been 6% (as inflation over this time has averaged around 3%). If you want to use the calculators to compare like with like, i.e. spending power now versus spending power in the future, you should use a real rate. Again you might need to reduce the rate to allow for the cost of investing.

Real rates of shorter periods have also been quite varied. Over 20 years, average real returns range between -2% and 13%. Over 50 years, the range is a lot narrower, at 4% to 9%.


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