Quick Guide to Calculating with the Rule of 72

What Is Rule of 72? : How to Use It and Flaws of Rule 72

No one can predict when your investment will generate income or whether it will be profitable. But no one has ever stopped trying despite that.

How can you reasonably predict the potential return that an investment could gain? One of the approaches is to look at interest rates on potential investments. The thing is, sometimes compound interest calculations can get complicated unless, of course, you have some calculator available.

Therefore, there is a "rule of 72". In an emergency, you might realise the interest in a particular investment over time. It's a helpful shorthand with many years in use. Let's explore the Rule of 72 examples and how it is calculated.

Key Highlights 

  • Although the Rule of 72 is approximate, it's a quick approach.
  • The Rule of 72 can be used to chart out the number of years it would take your investments without a set rate of return period. It can enable you to calculate what annual rate of return will be sufficient to make your goal achievable.
  • 5% to 10% is the rate-of-return range, whereby its calculation has much precision.
  • Divide 69.3 by the rate of return to get a more accurate result. It is true even though it may sometimes be mentally more challenging.

What is the Rule of 72, and how does it work? 

The Rule of 72 can calculate how soon your money will double at a given interest rate. How do we compute this rate? The number of years it will take your money to double is 72 divided by 4, assuming your account yields 4%. Here, eighteen years.

The same formula can also be helpful for inflation, but it will show how long it will take until the initial value is cut in half instead of doubling.

The Rule of 72 is only partially correct because it is an approximation developed from a more complicated computation. The Rule of 72 yields the most precise findings when applied to an interest rate of 8%; the results become less precise the further one deviates from this rate.

Nevertheless, this useful method helps you better understand the potential growth of your money based on a given rate of return.

How is the Rule of 72 calculated? 

This is how the 72-rule operates. If you take 72, you divide by the projected annual return on investment. This is the approximate number of years to double your money.

For instance, it will take about nine years (72 / 8 = 9) to double the invested money if an investment scheme provides an 8% annual compounded rate of return. 

Note that when an 8% compound annual return is set in this formula, it gives out the number 8 instead of 0.08, which makes the outcome nine years, not as against a result or lengthy period of 900.

If it takes nine years to double, the same $1,000 investment will be doubled into $2000 in 9 years, $4000 in 18 years, and $8000 in 27 years.

Rule of 72 formula & Example

This formula is used to determine fixed interest rates. Let us explain the Rule of 72: 

The Rule of 72 can assist in forecasting when an investment will double in value. This computation uses an expected interest rate for each period.

The following is the formula:

t = 72 / r

Where t is the number of periods needed to double the value of an investment

Where r is the percentage interest rate for each period.

It seems very easy. Enter 8% as the investment's yearly interest rate. 72 / 8 = 9. The current investment would take around nine years to double in value at the current rate, according to the Rule of 72. It is precisely 9.006 years.

The Rule of 72 is the most accurate, with an interest rate of 8%, but other percentages approach it. If the interest rate were 6%, it would take 12 years, but it's 11.896. 10% interest is 7.2, or 7.273 years, using the Rule of 72.

It is a useful rule to help you gauge the time it takes for an investment to double in value based on your interest rate. It may help you choose an interest rate to double your investment in a certain timeframe. 

Imagine you want your investment to quadruple in five years. It would help if you found x since 5 = 72/x. This technique suggests a 14.4% interest rate on this investment. This context also benefits from the 72 rule: Compound annual interest = 72/Years till investment doubles.

Rule of 72 compound interest

The Rule of 72 lets you anticipate how long an investment will double. The compound interest calculation determines future investment value.

The formula for compound interest:

A = P (1 + r/n)^(nt)

A is the investment's future worth, and P is the principal sum. r is the interest rate. n = The number of annual compounding cycles for the interest t = Years in a Time

By simplifying the previous calculation and assuming a constant interest rate and compounding period, we may derive the Rule of 72. This makes the formula as follows:

A = P (1 + r)^t

After taking the natural logarithm on both sides, we arrive at:

ln A = ln P + t ln (1 + r)

Using the first-order Taylor series approximation process, we can approximate ln (1 + r) as r. As a result, the formula becomes:

ln A ≈ ln P + r t

If we rewrite this equation, we obtain:

t ≈ ln 2 / r

Rule of 72: Better explained.

An online trading platform may help investors calculate the time it will take an investment to double, depending on the yearly interest rate. Dividing 72 by any financial instrument's yearly interest rate is easy for investors. The response gives projected investment doubling time.

Mathematics-wise, the Rule of 72 applies exclusively to assets with a fixed yearly return rate. Rule 72 best describes compound interest investment. When investing without a pre-arranged interest rate, the Rule of 72 may be applied by reviewing the asset and estimating its return. Fifteen per cent of annual returns can be calculated using the Rule of 72 from past performance.

Rule of 72 for money's value due to inflation

Investors may calculate the years it will take inflation to decrease their buying power in half using the Rule of 72. If inflation is 8%, 72 divided by 8% will show how long your money takes to lose half its value.

It takes nine years to lose half your purchasing power (72/8). Investors can determine how much inflation is by the Rule of 72. Even though the inflation has not been high for such a long time in the past, it was over several years significantly crippled assets ability to purchase power that had accumulated.

Rule of 72 proof

The Rule of 72 can be used to determine the doubling period in an investment and a quantity growing exponentially, like bacteria, money or people. 72 divided by the interest rate determines how many years it takes to double your money, depending on that particular place. 72 divided by 8 equals nine years at 8% interest for money doubled. The Rule of 72 approximates the natural logarithm formula for doubling time. The Rule of 72 is easier to remember and works best with 5%–10% interest rates. 

Is the Rule of 72 still accurate? 

Because the Rule of 72 is based on a more complex computation, it is an approximation that needs to be more accurate. When the interest rate is 8%, the Rule of 72 yields the most accurate results; the results become less accurate the further one deviates from 8%. However, if you use this useful formula, you can estimate how much your money might increase over time, given a specific rate of return.

What are the flaws of Rule 72? 

  • When the rate of return is between 6 and 10%, the Rule of 72 is generally correct. Any higher and the estimated value is subject to variation.
  • It can only provide a ballpark estimate of the time required to double the investment because it is inaccurate.
  • The Rule of 72 is null and useless if there is a change in the interest rate due to any reason. 
  • Investments with simple interest and those with fluctuating interest rates are not covered by the Rule of 72.

How do you reverse the Rule of 72? 

The following is the formula:

Annual rate of return compounded annually = 72 / Number of years needed to double the investment.

For instance:

Imagine receiving a Rs 100,000 bonus and wanting to increase it over the next decade.

Thus, by reversing the 72-rule,

72/10 – 7.2% is the compound annual rate of return.

A generalised annual rate of return is recorded for each mutual fund plan. This formula lets you find mutual funds with 7%–8% yearly returns.

Final Words 

So there you have it- everything about the Rule of 72, the Rule of 72 formula & examples. Before deciding on how much to invest, one should never forget the Rule of 72. If you start investing early, a relatively small amount can easily bring about effects. Still, when compound interest starts to take effect, the more money invested will only signal an increase in effectiveness. The Rule of 72 can also be used when determining how quickly your purchasing power may decline during inflationary times.

FAQs

In Which Case Is the Rule of 72 Most Correct?

Although the Rule of 72 only offers an estimate, rates of return between 5% and 10% yield the most accurate approximation. You can see from the chart in this article that computations lose accuracy as return rates fall outside that range.

Why is the Rule of 72 applied instead of 70?

Regarding annual interest rates, the Rule of 72 works best. Alternatively, semi-annual compounding pairs nicely with the Rule of 70. Consider a scenario where you have an investment with a 4% interest rate compounded twice a year or semi-annually. According to the 72 rule, you will receive 18 years.

What are the benefits of Rule 72 in finance?

Any investor may utilise it right away because it's straightforward. Investors can modify risk and holdings. Any market variable—GDP, population growth, etc.—can be utilised with an expected yearly interest rate. It lets investors determine their investment doubling time. Investors have a limited time to sell their securities and generate a two-to-one profit.

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10 Mar, 2024

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