The Rule of 70- Exponential Growth

The Most Important Rule You Will Ever Learn

Well, it is a rainy weekend here in New Zealand, so I thought I would share with you one of the most important things that you will ever learn about money.  And it is something that you all will know about, but just not understand properly. Or maybe you do, but hear me out anyway.

Everything is tied together with maths. And maths can be difficult. I will try to convince you that the greatest shortcoming of our entire world is our inability to properly understand the exponential function.

The Exponential Function

You will have heard about the exponential function. This the one that you write down to work out how much an investment will earn you, or how much debt will cost, over several years.  Say you have an investment that is growing at 5% per year, you write down the exponential function to work out how large it will be after, say 5 years

Ok, but with this steady 5% growth per year, do you know how to calculate how long it will take the original value to double?

We all need to know how to calculate how long an investment will take to grow to twice its size. That is a really important thing to know.

Lucky, it’s easy to work out. You just take the number 70 and divide it by the per cent growth per unit time.  This gives you the time it takes for your investment to double. For example, your investment of 5% per year will take 70 divided by 5 years to double. That is 14 years.

The Rule of 70

You might wonder were  70 come from the answer is, it is roughly 100 times the natural logarithm of 2. If you want you to work out how long it will take for your investment to triple you need to use 100 times the natural logarithm of 2, which is roughly 110. It’s all very logical.

You don’t need to remember any of this nerdy maths stuff. You just need to remember the number 70. Now, every time you make an investment or see a per cent growth, you can work out how long it will take to double your investment.

And if you want to be really clever, remember 110 as well.

Let’s run through an example, you read a story that house prices in NZ have been increasing by 7% per year, for several years. That doesn’t seem to sound too bad compared to the 20+ % increase we have been seeing in the news and media.

But you remember your rule of 70. Now at a price increase of 7%, it will only take 10 years for those houses to double in value. That is crazy!

Now an example outside of money and investments. You read that crime has doubled in a decade. You would think about what is going on! This is out of control. But what is going on is that crime has been increasing by 7% per year over 10 years.

Most people wouldn’t know what 7% growth really means!

Let’s take another example say from Mt Ruapehu. Their lifetime lift passes have been growing at around 5% per year since they opened.  In 1970 their lifetime lift passes cost around $350,  46 years later the price was 3950. Now, what do we have to look forward to the next time they offer lifetime passes for sale.

Let’s look at something that’s growing steadily after one doubling time the growing quantities

up to twice its initial size. Two doubling times it’s up to four times its initial size then it goes to eight 16, 32, 64, 128, 256, and 512, in just 10 doubling times it’s a thousand times larger than when it started!

From 1970, at 5% growth, the lift passes doubled in roughly 12 years in 1982 (70 divided by 5% growth), then 4 times the in the year in 1994, then roughly 8 times in the year 2006. Last time they were on sale in 2016, the price was $3950. 11 times what they were in 1970.

If this rate continuous, in 2018 they are expected to be at least 12 times their original price at $4200, and in 2030 they will be 16 times, and in 2048 they will be 64 times their original cost at a whopping $22,400. And that is just 5% growth!

So next time you see an interest rate, calculate how long it will take to double your investment. Just remember to divide 70 by the interest rate. This gets you the doubling time. Double the doubling time and you will have the number of years it will take for your investment to be four times the original amount. And so on.

This is the rule of 70, and anyone wanting to grow passive income needs to learn it! But always sort out your emergency fund before investing.


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