Rule Of 72 Formula

Article byWallstreetmojo Team
Edited byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

What Is The Rule Of 72 ?

Rule of 72 refers to an approximate approach to determining how much time long-term investment will take to get double value at the fixed interest rate and is calculated by dividing the annual interest rate by 72.

Rule of 72

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Even though it provides an estimate or an approximate value for the purpose, it is widely used for making instant mental calculations when investors wish to find out the effect of compound interest or growth. It is quite popular in the financial world but works best in the case of some particular range of growth rates or interest rates.

Key Takeaways

  • The Rule of 72 is used to estimate how long it will take for your long-term investment to double in value. Just divide 72 by the annual interest rate.
  • As an investor, it’s essential to calculate the rate of return. To find out when your investment will double, divide 72 by the rate of return.
  • Learning useful formulas can provide investors with quick and helpful results, even if they have little prior knowledge of investing. Although the Rule of 72 is practical, it should not be considered a replacement for financial ratios.

Rule of 72 Formula Explained

The rule of 72 formula is a widely used and instant method used to evaluate the period or how many years an investment will need to double the amount using a particular rate of return. In simple terms, it helps us understand when we can double our funds.

There are various sophisticated financial tools and rule of 72 formula calculator which help in the calculation of formula for rule of 72 especially if the rate of return are varied and the financial scenarios are complex.

As an investor, you need to know the rate of returnRate Of ReturnThe real rate of return is the actual annual rate of return after taking into consideration the factors that affect the rate like inflation. It is calculated by one plus nominal rate divided by one plus inflation rate minus one. The inflation rate can be taken from consumer price index or GDP deflator.read more. And then, all you need to do is to take the number 72 and divide it by the rate of return. And you will get the duration of time that will double your investmentTime That Will Double Your InvestmentThe doubling time formula measures the time taken by an investment to become twice its present value. Doubling Time = ln 2 / [n * ln (1 + r/n)]; where r is the rate of return and n is the number of compounding period per year.read more.

Rule of 72 = 72/r

Here, r = the rate of return

Alternatively, there can be another 72 rule formula.

Here, you would be able to know the rate of returnRate Of ReturnRate of Return (ROR) refers to the expected return on investment (gain or loss) & it is expressed as a percentage. You can calculate this by, ROR = {(Current Investment Value – Original Investment Value)/Original Investment Value} * 100read more at which you would be able to double your investment.

Alternative formula

Here. t = duration of time

Example

Let us understand the concept of formula for rule of 72 with the help of a suitable example.

You can download this Rule of 72 formula Excel Template here – Rule of 72 formula Excel Template

Deeds Inc. has been offering a 9% return on the investment of $200,000. Find out when the money will get double. Also, if the investors want to double their money in 6 years, what would be the available rate?

By using the first formula of 72 rule, we get –

  • = 72 / r = 72 / 9 = 8 years.
  • It will take eight years to double the money.

Coming to the next question, we can use the second formula of Rule of 72.

  • = 72 / t = 72 / 6 = 12%.
  • At a 12% rate, the investors can double the money within six years.

The above example and explanation clarify the concept with the help of a suitable case study. The case study shows two different scenarios where the same formula has been used to solve two different problems successfully.

Interpretation

Let’s understand the above two equations in detail.

The first formula is all about “when.”

And the next formula is all about “what rate.”

  • In the first formula, the investor isn’t sure about the time duration of the investment. She needs to use the formula to conclude.
  • In the second formula, the investor isn’t sure about the rate of return on the investment. In other words, in the second formula, the investor isn’t sure at what rate she would be able to double her investment.

As an investor, you should use both.

  • Let’s say that you’re investing $100,000 into an investment. They are offering you a 10% return.
  • Using the first equation, we can easily determine when you will double your investment.
  • = 72 / r = 72 / 10 = 7.2 years.
  • Let’s say the investor wants the money to double within six years.

What should she do in that case?

  • She needs to use the second equation to reach a conclusion.
  •  = 72 / t = 72 / 6 = 12%.
  • To double the money the investor puts into the investment within six years, she needs to get a rate of return of 12%.

Use And Relevance

The concept of rule of 72 finance formula has some important uses as follows:

  • If an investor needs to know the basics about the investments, they should have useful formulas and, at the same time, can deliver quick results. It is very useful and can help investors quickly.
  • Even if the investors don’t know anything about investment, they can quickly use these formulas to know the basics of the investments. However, the rule of 72 can’t act as substitutes for financial ratiosFinancial RatiosFinancial ratios are indications of a company's financial performance. There are several forms of financial ratios that indicate the company's results, financial risks, and operational efficiency, such as the liquidity ratio, asset turnover ratio, operating profitability ratios, business risk ratios, financial risk ratio, stability ratios, and so on.read more.
  • It helps in planning for meeting the financial objectives in the long run because it provides a rough estimate about the future projections of wealth creation.
  • It is a very good method for comparing investment opportunities available in the market. Different rate of return can be used to determine which financial opportunity will successfully double the money within the shortest period.
  • It is an effective way to understand the concept of compounding which shows how funds grow exponentially during reinvestment. Thus, it can also be considered an educational tool for teaching the compounding method.
  • The rule of 72 finance formula comes as a very handy method of making mental calculation easily.
  • It can be applied to different macroeconomic concepts like estimating the time needed for an economy to double its size or population, or used to estimate how long it will take for the value of money to become half of what it is currently due to rise in inflation, etc.
  • It is also successfully used for savings and retirement planning. Since the formula finds out the time to double the money, it gives an idea about how much funds will be accumulated by the time a person is retired.

Calculator

We can use the following rule of 72 formula calculator.

Rate of Return (r)
Rule of 72 Formula =
 

Rule of 72 Formula =
72
=
Rate of Return (r)
72
= 0
0

Calculation in Excel

Let us now do the same example above in Excel.

This is very simple. You can easily calculate the ratio in the template provided.

Rule of 72 in Excel

Frequently Asked Questions (FAQs)

What are the limitations of Rule of 72?

One significant drawback of the Rule of 72 is that it assumes a consistent interest rate, which may need to be revised. Interest rates can fluctuate, affecting the precision of the Rule of 72 calculation.

Who introduced the Rule of 72?

The Rule of 72, commonly attributed to Einstein, was most probably discovered by an Italian mathematician, Luca Pacioli, in the late 1400s. In addition to this, Pacioli is also known for inventing modern accounting.

Why is the Rule of 72 helpful in choosing an account for your money?

The Rule of 72 calculates how long it would take to double your money in a savings or investment account that earns interest. You can use this Rule to determine how much your money can increase based on the interest accumulated in a savings account.

Recommended Articles

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