## How can you use rule 72?

**Basically, if you want to know how long it takes to double your money, Rule 72 is helpful.**

I will illustrate its use through a few examples.

On the Investments page, I wrote about when Rule 72 will help you.

## How do you use Rule 72 to quickly find out which investment will double in how much time?

You have three investment options. For simplicity, all three have a guaranteed return.

It brings

1. 4%,

2. 6%, and

3. 9% net annually.

Logically, everyone would invest in option 3, but let’s see how much more advantageous it is in terms of time frame.

Let’s say you don’t have an investment calculator, an excel spreadsheet, but not even a checkered paper. For example, you talk to your friends and talk in the meantime.

Number | Annual yield | Year required for doubling |

1 | 4% | 18 év |

2 | 6% | 12 év |

3 | 9% | 8 év |

A strength of 1% can mean many, many years. If you only get 3 instead of 4%, it takes 24 years to double.

6 years can mean a lot, think about where you will be in your life when you double with one and when you double with the other. This can be especially important if you are saving for a specific goal (So you need X for the end of a certain period.)

### How can you easily calculate how much time it takes to double down?

You can calculate this very easily, even in your head:

72 /% growth.

In our example:

72/ 9 = 8

Pay attention to one thing, and the time period: if the yield is % / year, then the time will come in a year.

**Let’s look at rule 72 in terms of the growth required!**

You can also use the same method backwards to see how much growth a given capital needs to spend a certain amount after a certain amount of time. (Eg how much should your current money grow to buy something in X years?)

This is not true for only money, e.g. what percentage of my email subscribers need to grow to double that in 18 months?

72/18 = 4 % / month

That is, with rule 72, you can calculate any increase, whether the rate of growth is an issue or the time required. It is not necessarily only for money, although it is a fact and real, it matters most when it becomes more.

### An important addition to duplication:

Suppose you play with the numbers and it turns out that your investment will double 3x by the time you reach the target date. What it means?

Let’s say your starting capital is 1.000.000 forints, and you double that.

Doubling 1x is not a problem for many people, they immediately say it is 2.000.000.

In the case of a triple doubling, however, 3.000.000 is a bad answer. Forget it: 3.000.000

1x doubled: 2.000.000

2x doubled: 4.000.000 (since 2.000.000 are still working here)

3x doubled: 8.000.000

And this is nothing but the power of compound interest.

## A little math behind rule 72. Or: why does rule 72 work?

The whole is based on the formula for calculating future value. The formula that shows how much of your money will be with interest at a given time. The formula for this is:

FV = PV * (1+r)^{n}

What is covered in the formula:

PV: the capital you still have, that is, the present value

FV: the capital you will have

r: the interest rate at which your money increases

n: that’s how long you’ve been working on your capital.

Replace with the simplest numbers. Since we are looking for a doubling, we can also take into account that you want to see 2 out of 1 forint, and it is a question of when this will happen at a given interest rate.

Then the present value will be 1 and the future value will be 2.

2 = 1 * (1+r)^{n}

Since multiplication by one does not divide or multiply (i.e., multiply but only by one, but it is not…, na anyway, let’s scroll), we can omit:

2 = (1+r)^{n}

Now, instead of going very deep into it, I ask you to either accept the authenticity of this step or contact your math teacher.

Since we are looking for time here, so n is the question, so we are curious about the value of the exponent. The natural logarithm is used for this.

ln 2 = ln(1+r)^{n}

ln 2 = n * ln(1+r)

0,693 = n*r

n = 0,693/r

Then you either express the interest as a decimal fraction, i.e. you perform the 0.693 / 0.1 operation at 10% annual interest, or you multiply it by 100, i.e. 69.3 / 10%.

However, this is very difficult to count, especially in the head. So smart people were looking for a number that is very close to that value but has far more divisors. **And this is nothing but 72.**

## In this article, instead of the usual “Questions”, the “homework” associated with the use of Rule 72

You plan to take out a HUF 10 million dividend from your business over time and want to know what you need to do in one case or another. How do you use rule 72 to calculate what you need to do is worth it to you?

- What is the average return you need to achieve in order to withdraw such an amount from the 1 million forints allocated for this purpose today in 10 years?
- If your expected annual return is 8% and you want to see the amount in 5 years, how much do you need to set aside today?

**A little help if you get stuck:**

### Solving example 1

1 million initial capital

1x doubled: 2 million

2x doubled: 4 million

3x doubled: 8 million,

and for that we still need a quarter of 8 million. Since we have 10 years here, the question is how much money must grow on average in 1 doubling in order to withdraw 10 million after 3.25 cycles for year 10. As you can see, the 72 rule is not a straight line (non-linear), so using annual interest rates is mostly a guide. If you want to calculate such a high yield, Rule 72 requires a monthly breakdown to clarify.

Let’s see if we want to get results on an annual basis.

If I want to double my money 3.25x in 10 years, then on average I have to double in 10 / 3.25 = 3.07 years every time.

72/3,07 = 23,4 % / year

If we ease a little bit and say that the 3 doubles are still few, we need a 4 as well, then 10/4 = 2.5 I need to see twice as much money every year.

72/2,5 = 28,8 %/év

Although the exponential function is a bit difficult to use as a “DIY” method, you can see from the past whether you jump into it or not.

**If you are very attached to the exact calculation**** : **

A little more clarification to see how much it means to think for years on such a function for years or months:

10 years is 120 months. If 120 / 3.25 = 36.9, then we want to see 2x as much money every 37 months.

72/37 hónap = 1,95% / month

(The doubling comes out on control calculating, provided you capitalize on a monthly basis)

Checked by a compound interest calculation, the expected return is about 32%, but here it seemed from the beginning that you have to set aside not 1 million in total if you realistically want to take out 10 million after 10 years.

The annual yield of the example pushes the limit of viability, I have seen it more than once. But there is, of course, no guarantee that this will always happen for 10 years. So it is useful to think about it properly, wether anyone promise anything.

### Solving Example 2

Slightly more twisted: 72/8 = would double 1x in 9 years with 8% yield. If we had 9 years, we would need 5 million forints. But that’s not all here.

The question here is how much is missing for the 1st doubling. It would take another 4 years, so the 5 million should be “added” to this.

4/9 = 44,44%

5.000.000 Ft * 44,44% = 2.222.222,- Ft

Thus, the answer: HUF 7.222.222 is the initial capital.

If you are familiar with present value and future value calculations, you can use it for verification. Here, however, notice that rule 72 is present as a rule of thumb, so while the calculation will come out roughly, you will experience some discrepancies in the end result.

As you can see, the second is a more realistic idea. If you want to make a dividend, this makes it relatively easy to plan your basics. For the rest, let’s say it doesn’t hurt to have some experience.

If you have any questions or would just like to comment, please leave a comment or contact us in person.

You can access this article in Hungarian and German | |
---|---|

Mi a 72-es szabály? | |

Was ist die 72-er Regel? |