The Rule of 72

The-Rule-of-72

(credit: Swan Retirement)

Compound interest – Albert Einstein once called it one of the most powerful forces in the universe. But it’s extremely difficult to deal with in cases (and on the McKinsey PST for that matter) because you don’t have access to a calculator.

So what do you do if you’re asked to deal with compound interest in a case? Easy, use the Rule of 72!

In today’s article we will talk about what the Rule of 72, where to use it, and its implications.

What Is The Rule of 72?

As it says above, the Rule of 72 says that when you’re dealing with compound interest, you can estimate the number of years N it takes to double an investment which is growing at an annual rate R by N = 72/R.

For example, if your money is growing at 6% annually, it would take 72/6 = 12 years for it to double.

If you’re curious how long it would take to triple, it’s 114/R, and to quadruple it would 144/R.

Instead of 72 as the base you could also use 69 or 70, apparently 69 is the most accurate base but they chose 72 because it’s divisible by the most numbers.

When to Use It?

You can use the Rule of 72 any time you have to deal with compound interest or when comparing investments. For example, sometimes you have investments that start at different years and you need to compare how much they’ll be worth in the future.

For a simplified example, let’s say you can make an investment A today with a principal of $50,000 today which will grow 12% annually. Let’s say you can also make an investment B at year 6 with a principal of $200,000 which will grow at 6% annually.

What will these investments be worth in year 18? (I know it sounds like a strange example, but imagine investments A and B are types of wines that grow in value as they age).

Year Investment A ($) Investment B ($)
0 $50,000
6 $100,000 $200,000
12 $200,000
18 $400,000 $400,000

Strangely enough, in 18 years time they’ll have the same value, despite the fact that the principal of investment A is much smaller (again, the magic of compound interest).

Implications

There’s a significant difference between a 1%, 2%, and 3% growth rate. Why? Because under a 1% growth rate, it’ll take 72 years for something to double. With a 2% growth rate, 36 years. With a 3% growth rate, 24 years.

That’s why people make such a big fuss about the fact that the US’s GDP growth rate is only 2-3% and that in developing countries it’s 7-8%. It doesn’t sound like a big difference but because of the magic of compound interest it can quickly amount to big differences.

Conclusion

The Rule of 72 can help you predict how long it will take something to double with a set annual growth rate. You can use it to make estimates about doubling time, compare investments made it different times, and make sense of compounded numbers.

And don’t forget the magic of compound interest. Even a small change in something’s growth rate (i.e. from 1% to 3%) can have a significant impact on its doubling time.

Good luck!

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