THE RULE OF 72

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I know you want to double your money. This is the excuse most people make to go on a gambling spree. When I used to play table tennis or ping pong as they say in some parts of the world, we sometimes do a friendly bet. When you hear double or nothing, take your win and run! This is when you know you are about to get hustled. It turned out some professional players will intentionally lose the first few games and then ask you to go all in, double or nothing. If you fall into the trap, they will crush you 21 to zero. 

Well, before you run, I would like to take you through an important concept in finance -The rule of 72.

 

I will go through how the rule was derived. You will be surprised to hear that 72 was just an approximation and not the original number. Read to the end to enjoy the mathematical higgledy-piggledy.

 

 

The Rule of 72 in Investment

The Rule of 72 is used to estimate the doubling time of investment. Divide the number 72 by the interest percentage per period in order to get the approximate number of the period required to double your investment.

 

It’s a simple way to access your investments. This way, you can focus on looking for investments that will generate more money for you instead of depositing your money in the bank for only 0.01% interest.

 

You will never double your money in your lifetime with that interest rate, so don’t bother calculating. We discussed that in one of the rules of money, not letting your money get bored in bank accounts. 

 

What is the Rule of 72 Formula

N = 72/R

R = rate of return

N = the number of time period the money is invested.

 

 

 

 

Why You Should Learn the Rule of 72

1. It let you know when your investment will double

If you want to know how long it will take for your investment to double at a specific annual compound interest rate, you should use the Rule of 72.

 

This will motivate you to improve your efforts in saving for retirement.

 

For instance, if your retirement savings are returning 7% yearly, it would take 10.3 years for your money to double. Just divide 72 by 9, and you will get the result.

 

2. The rule of 72 let you estimate your return if you know the timeline

You can also use the Rule of 72 to determine what interest rate or annual growth you have to double your money within a specific number of years.

 

For example, if you want to double your investment in 5 years, you have to divide 72 by that number, and you will get a 14.4% rate of return.

 

The Rule of 72 is pretty accurate for investments that offer between 6% and 10% of growth rates. However, the higher the rates, the less accurate the results will be.

 

 

3. The rule of 72 can inspire you to save more

One of the best things about the Rule of 72 is that it helps you save more by starting earlier.

 

If your investment could double every 5 years, you will have more time to grow your investment.

 

You should start saving for your retirement as early as possible, so you don’t need to worry about your lifestyle in your golden years. You can live comfortably using the money you have saved.

 

 

4. The rule of 72 let you pick an optimal investment strategy for your goal

By using the Rule of 72, you can invest in the best investment options to achieve your financial goals faster.

 

For instance, if you invest in top mutual funds that offer 12% to 14% annualized returns, you can double your investment in 5 to 6 years.

 

If you want to double your money in 3 years, you have to find an investment option that offers 24% returns. Sector-based funds, stocks, and mid-cap funds usually offer such returns but are not consistent.

 

These options are ideal for high-risk takers. The higher the yield, the higher the risk as discussed in the richest man in Babylon.

 

The Rule of 72 is also beneficial for non-finance individuals as there is no need to do any complicated calculations.

 

Beware!! do not read this section if you are afraid of mathematics.

A little background derivation of rule of 72

I was a mathematician in my former life. Some might say, once you are a mathematician, you are always a mathematician.

Let me enjoy myself for a few minutes, ok! The first thing to know is that the number was not originally 72. It was 72 to make it easier for people to calculate.

If you hate mathematics, please go ahead and comment and pin my pics to Pinterest. Don’t forget to subscribe too.

 

 

 

Rule of 72 (oops 69.3) proof

Starting from our “time value of money” formula, we have.

FV = PV X (1 + R) ^N

FV = Future value

PV = Present value

R = rate of return

N = the number of time period the money is invested.

To double your money, we will assume you start with 1 dollar and you want to double it to 2 dollars.

The equation becomes

 2 = 1 * (1+R)^N

2 = (1+R)^N

Now we apply natural log to both sides

ln(2) = ln( (1+R)^N )

.693 = N * ln(1+R)

For small R, or if R approaches zero, ln(1+R) ~ R

.693 = N * R

.693 / R = N

N = 0.693/R

To make the right side an integer, we multiple the right side by 100

N= 69.3/R

We are not done. As you can see, 69.3 is not sexy. To make it easier to use and more palatable to the eye, the closest number is 72 as it is much more divisible.

Hence the formula for the rule of 72

N = 72/R

You either enjoy that section or got dizzy, either way, you survived. You can also use the rule of 72 calculator if you don’t enjoy division. 

 

Conclusion

The Rule of 72 helps you understand the importance of saving and how much your savings can increase through compounding. Just keep in mind that all investments are risky, so you have to educate yourself on the right plan of action. This way, you can retire comfortably without worrying too much about your finances. Use the Rule of 72 to get an idea of how long it will take your investment to double at your present rate of growth. The results could help you determine if you have to improve your retirement savings game.

 

Other posts that touched base on the rule of 72. 

6 times you should not buy a house

Everything you need to know about 401K

Also, try out our compound interest calculator to see when you will make your first million 

The importance of time value of money

 

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