When I was at secondary school, one of my favourite subjects was maths. I remember practicing hours to have a good performance. There was one thing that I learnt very young in that class that changed how I think of money: double investments.

First things first. When I was at secondary school, we were not allowed to use the calculator except for few exceptions. So, it was normal to create some mental maths shortcuts. There was one particular shortcut that stayed in mind forever. The Rule of 72.

1. What’s the Rule of 72?

It’s a mental shortcut to calculate how many years it will take to double your investments given a certain interest rate. I mentioned it last weekend in my newsletter and some time ago in my career talk at the University of Greenwich but the idea behind the below formula is to explain in very simple terms the concept of compound interest.

The formula is simple: 72 / Interest Rate = Years to Double Investments

For example, it will take me 12 years for my investment to double if they grow at 6% (72/6=12). But it will only take me 9 years if my investments grow at 8% (72/8=9) and so on.

2. Where Else Can I Use It?

Economy growth, supermarket, college tuition and most of the daily life. Don’t believe? Let’s see some examples.

The economy of your country will double in 18 years if it grows at 4% annually. Why? Again, 72/4=18.

You’ll lose half of your money in 24 years if the inflation goes from 2 to 3% in a year. Why? One more time, 72/3=24.

Do you have kids? Then remember this. Tuitions costs will double in 9 years if they increase at 8%. This is faster than inflation and if you have credit cards it can get worse. How much is your interest rate? Imagine 15%. OK, then your debt will double in less than 5 years!

3. I Still Don’t Believe. How Do You Explain It?

Alright. Here we go. Let’s imagine you have $100 and your annual interest is R. Then after one year you’ll have 1 x (1+R). If the interest is 10% then your $1 x (1+0.1) equals $1.10. This is Year 1.

In Year 2, you’ll have 1 x (1+R) x (1+R) or simply 1 x (1+R)^2. Following the sample example with 10% interest, then $1 (1+0.1)^2=1.21.

Now, you get the concept of compounding interest. You’re actually making money!

How many years it will take for your $1 to become $2?  Following the same analysis, assume that N is the number of years you want to calculate. These are the steps:

1st Step -> 1 x (1+R)^N = 2
2nd Step -> (1+R)^N = 2
3rd Step -> ln((1+R)^N) = ln(2) -> this is a natural log on both sides
4th Step -> N x ln(1+R) = .693
5th Step -> N x R = .693 -> note that when the interest R is small, then ln(1+R) ~ R
6th Step -> N = .693 / R
7th Step -> N = 69.3 / R -> we multiply by 100 as we want the interest R as integer

Because we want a nice number to be able to divide, we need to either use 69, 70, 71 or 72. Which one has more factors to be divisible? Either 70 or 72. We could use both to be honest but it’s much easier 72 as it’s more divisible (2,3,4,6, etc.).  

Final Thoughts

As you saw in the 5th step, we did an approximation and when the rates are higher, the formula can be less accurate. But still, it’s about having a quick mental shortcut.

I learnt this when I was a teenager. Years later when I went to University and started to review financial maths, things were more intuitive as I unconsciously learnt years before the power of compounding interest.

I’m a simple guy. I don’t like complicated things. So, these shortcuts are a great way to make your own judgment before going to an expert.

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