The Rule of 72 and how this applies to you

How long does it take to double your investment?Hello friends,

When it comes to investing, there will be many reasons to invest : Are you investing to achieve your financial goals (buy a Tesla S within 2 years, spend your 3 months mini-retirement in Sevilla sponsored by dividends only,…)? Are you investing to prepare for retirement?…

The important part is to have a purpose for your investment.

After you have gone through an investment proposal and decide this will provide you with a good return on investment you might want to be able to evaluate quickly how long it will take to double, triple or even quadruple your initial investment.

Let’s say you need 30 000 EUR for the downpayment for a house you plan to buy in 3 years and today you have 15 000 EUR available. You are considering an investment of 15 000 EUR in an index fund* that reproduces the S&P500 offering you a 9% annual rate of return . When will that investment grow to 30 000 EUR and will you be able to have the downpayment ready within 3 years?

From the looks of it 9% is a fairly high return on investment compared to other investments such as long-term Treasury bills (2-4%), Real Estate (4-7%),… You can start calculating based on future value formulas when your investment will double. Here is the formula for those who want to practice : PV*(1+r)^n=FV where PV is the present value, r is the annual rate of return, FV is the future value and n the number of years.

But with the rule of 72 in mind, it is quicker to see that you will need 8 years to double your investment. So if you want to gather the additional 15 000 EUR within 3 years, you will need to start saving at least 3 525 EUR per year in addition. Please bear in mind that the 9% return on the index fund is a historical average.

  • What does this rule of 72 entail?

In short it is a simple way to quickly estimate how long it will take for your investment to double in size, provided that you reinvest the returns/dividends. Just keep in mind that this will give you an approximate figure. To calculate this easy formula you only need the annual rate of return.

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Our annual rate of return was 9%, so 72/9= 8 years.

Conversely you can estimate what your annual rate of return should be, given your time frame. In the case above we would need to find an investment opportunity that provides a 24% annual return on investment to double our investment from 15 000 EUR to 30 000 EUR. If you know of any such investment, feel free to comment below! I am all ears.

  • Below you will find a few interest rate with the associated time it takes to double your investment :

1% – 72 years

2% – 36 years

3% – 24 years

4% – 18 years

5% – 14 years

6% – 12 years

7% – 10.3 years

8% – 9.0 years

9% – 8.0 years

10% – 7.2 years

11% – 6.5 years

       12% – 6.0 years

  • For the number geeks among us (I am one too!) :

It all comes from this equation PV(1+r)^x=FV=2PV, and by using logarithms you will come to the result : x=72/r. You can find the demonstration here.

  • How long does it take to triple and quadruple my investment?

Based on similar approaches you can use the rule of 115 for tripling and 144 for quadrupling your investment.  If you are investing with an annual rate of return of 5%  you will hence double your investment in 14.4 years/triple in 23 years and quadruple in 28.8 years.

  • The rule of 72 in reverse

Another way to use this rule is to use in in other contexts : How long will it take for my bottle of milk to double in price? If we look at a long-term inflation rate of 2,5-3% annually, we can estimate that 24 years from now we will pay the double for it. When will the population of country XYZ with a current population growth of 2% double? Short answer within approximately 36 years.

One of the things that I particularly like about this rule besides the quick calculation is that it is often easier to relate to a 6 or a 9 years doubling time than an annual return of 12% or 8%. Do you think so too? Just think of how far you are from retirement and about your investment goals, can you use the rule of 72 to redefine your investment choices? I am sure you can.

I must admit this post was rather geeky but I hope it will help you in defining your investment priorities. Now go and impress your friends or manager with your incredible calculation speed! If you have any questions or comments feel free to leave me a message below.

*”An index fund is a type of mutual fund with a portfolio constructed to match or track the components of a market index, such as the Standard & Poor’s 500 Index (S&P 500). An index mutual fund is said to provide broad market exposure, low operating expenses and low portfolio turnover. These funds adhere to specific rules or standards (e.g. efficient tax management or reducing tracking errors) that stay in place no matter the state of the markets.” (Source : Investopedia)

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