How often have you heard an investment pitch that claims you can “double your money in five years”, or similar? Today we look at what those kinds of claims mean. The time it takes for something to double in size is known, unsurprisingly, as the doubling time. The maths that’s involved in calculating a precise doubling time is fairly complex. Fortunately there’s a handy and easy-to-use rule of thumb that gives us a reasonably accurate answer in seconds.
The investment world is curved due to something called profit compounding. This is the idea that if you reinvest your profits then there will be additional money made on that new investment, over and above the return on the original capital.
The crucial thing about compounding is that there isn’t a linear relationship between the rate of return in one year and the end result after many years of investment. Every incremental change in the annual rate of return will have a much bigger impact on the long term result. The longer the time period, the bigger the effect.
If you invest $100 and earn a consistent 5% a year, with profit reinvestment, after 20 years it will be worth $265. That’s a total profit of $165. If you invest $100 and earn 10% a year, also with reinvestment, after 20 years it will be worth $673, which is a profit of $573.
The longer the time span the bigger this disparity. This is compounding at work.
In this example the annual rate of return has doubled – from 5% to 10% – but the profit after 20 years is almost 3.5 times as much. The longer the time span the bigger this disparity. This is compounding at work.
Below is a chart which shows how a $100 investment would grow over 20 years, at steady rates of return ranging between 1% and 10% a year (1% is the lowest line, 2% next, and so on up to 10% at the top). It shows how the curves become progressively further apart, and at an accelerating rate.
So that’s a quick refresher on compounding. It’s explained in more detail in chapter two of our free Wealth Workout report that you received when you signed up for the OfWealth Investor Thought Club. If you’re not familiar with this essential investment concept, or would like more details, you can check it out here.
Linked to compounding is the idea of doubling times. A doubling time is simply the amount of time that it takes for something to double in size at a fixed rate of return. When it comes to investment, it’s usually expressed in years.
In the chart above the line growing at 10% a year doubles from $100 to $200 in 7.3 years. The 5% line doubles in 14.2 years. In other words multiplying the rate of return by exactly two cuts the doubling time by a little under a half.
If you understand doubling times then you understand why low rates of consumer price inflation are so important.
If you understand doubling times then you understand why low rates of consumer price inflation are so important. For example, consumer prices in the USA rose at 2.7% a year on average in the 26 years between 1988 and 2014.
That also happens to be how long it took for prices to double in US dollar terms – or, put another way, for a dollar to lose half its purchasing power at a 2.7% inflation rate.
But if inflation ran at 5% a year then prices would double every 14.2 years. At 10% inflation the price of a cup of coffee would double every 7.3 years. So, take pity on the poor Argentine. In recent years, with peso price inflation running at around 35%, prices in Argentina double in under two years and four months. That’s a tough environment in which to save and invest, and preserve wealth.
Here’s a chart that shows doubling times in years (vertical axis) for rates of growth from 1% to 20% (horizontal axis). Because of the compounding effect, you can see that this is also a curve, and not a straight line relationship.
Understanding doubling times is a very handy thing for investors. If you stand to make 8% a year after taxes and other costs, with all profits reinvested each year, your investment will double in 9 years. If you only make 2% net then the doubling time shoots up to 35 years.
Notice also that when rates of return are low, even small changes have a huge impact on the doubling time.
Notice also that when rates of return are low, even small changes have a huge impact on the doubling time. If you’re only making 2% a year then the doubling time is 35 years. Then if you manage to add 1% a year, and make 3%, the doubling time drops dramatically to 23.4 years – a fall of 11.6 years.
But if you’re already making 8% a year, adding 1% more has much less impact. At 8% the doubling time is 9 years. At 9% it’s 8 years, an improvement of just one year.
This provides a good argument for why investors should get out of very low return cash and bonds and into baskets of high quality stocks (bought at the right price) and other higher return investments. You’ll double your money much more quickly that way. (Although, of course, you still need to stay diversified.)
But, beyond a certain level, trying to squeeze out even higher returns is hardly worth the trouble. Think about that the next time someone tries to talk you into expensive, unproven, and very high risk technology stocks. Striving for extra returns from an already decent base may have little impact on your doubling time, and could in fact backfire in the form of big losses.
Working out precise doubling times requires quite fancy mathematics. But there’s a really useful and easy shortcut which I’ll explain.
(The maths involved uses something called logarithms. These are very rarely used by most people in their everyday lives. So even students that excelled at mathematics in school will most likely have forgotten the rules of logarithms within 10 years or so. Like all knowledge, if you don’t use it you lose it.)
The shortcut is called “the rule of 70”. The doubling time, expressed in years, is simply the number 70 divided by the annual rate of growth. So if an investment makes 10% a year it will double in size after roughly 7 years (70 divided by 10). An investment making 14% a year doubles in roughly 5 years (70 divided by 5). It’s as simple as that.
This rule isn’t perfectly accurate, and it becomes less accurate as the rate of growth increases. But it’s pretty close, and a handy way to quickly work out roughly what’s at stake. It’s accurate within 5% tolerance up to rates of return of 12% a year, and within 10% tolerance up to rates of 25% a year.
Also you can switch it around. If someone claims they can double your money within 3 years, using this rule means the claimed compound return is about 23% a year (70 divided by 3 years equals 23.3%).
You can then ask yourself whether that sounds reasonable for the investment being offered. Bear in mind that over the very long term the US stock market has returned 9.4% a year, on average, including both capital gains and dividend income – and before taxes and costs.
The rule of 70 is an incredibly simple and useful little rule of thumb to put into your investor toolkit. Start using it today.
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