The world of finance is complex, but sometimes you encounter calculations that are simple and very interesting to know. Today, I’m going to introduce you to the 72 rule and give some examples of calculations. Before I start, I always find it interesting to know the history of this rule. Indeed, this rule was discovered by the famous Albert Einstein during the Renaissance. Mr. Einstein declared:

Compound interests are the greatest force in the entire universe.

and

Compound interest is the eighth wonder of the world. Whoever can understand compound interest benefits from it, whoever doesn’t… pays for it.

## What is the purpose of this rule?

With this rule, you can find out how many years it will take to double the initial value of an investment. Useful, isn’t it? Take the following case: you have just invested 5’000 CHF in an account and you would like to know in how many years the capital will be 10’000 CHF. To get the answer, you will use this famous 72 rule. Note that this is valid for investments using compound interest of course.

## What do I need to know to make this calculation?

Obviously, every mathematical formula has variables and it is necessary to know some values of these variables.

• Annual rate of return on the account

The rate of return depends on your investor profile, your risk tolerance and the investment product you have chosen. In general, the more “risky” the product you choose, the higher is the theoretical return announced. Don’t forget that it is never guaranteed. Conversely, the safer a product is, the lower its potential return. This relationship is therefore inversely proportional.

Generally, to find out the performance of a product, simply consult the product sheet or speak directly with a consultant.

## The rule and the calculation

As I said, this calculation is very simple. Here is the formula:

period = 72 / rate of return

Note that this formula is really used in finance, but sometimes, instead of 72, the value of 70 is taken. According to some sources, it seems that the rule 70 is the evolution of the rule 72. The result, contained in the variable “period”, is often in years and is linked to the rate of return, which is also expressed in years.

Example 1 – Knowing the number of years to double your investment

Imagine that you have invested 5’000 CHF at an annualized rate of 6%. It will take you 72 / 6 % = 12 years to get 10’000 CHF. If you do the calculation with 70, you will get 11.6 years.

Example 2 – Knowing the return rate needed to double your investment after a specific number of years

The formula can also be reversed to determine at what rate you should invest your money if your goal is to double your investment after x years. Let’s say you want to double your investment after 6 years. The formula becomes :

rate of return = 72 / period

Using this formula, you would get 72 / 6 years = 12%. So you need to find a service that you believe can generate an annualized rate of return of 12%.

## Bonus Video

I hope you enjoyed this short post and that you will think about this formula when you are investing. As a bonus, I’m posting a little video (in French sorry) that explains this famous rule in a more mathematical way. This video allows you to understand the origin of this approximation formula.