What Is the Rule of 72?

The Rule of 72 is a simple way for an investor or advisor to calculate how long an investment will take to double, based on its fixed annual rate of return. Simply divide 72 by the fixed rate of return and you'll get a rough estimate of how long it will take for your portfolio to double in size.

However, the science is not exact and you may want to use a different formula to account for rates of return that are outside of a certain range.

What is rule 72?

The Rule of 72 is a rule of thumb that investors can use to estimate how long an investment will take to double, assuming a fixed annual rate of return and no additional contributions.

If you want to dig even deeper, you can use the Rule of 115 to determine how long it will take to triple your investment.

These two basic rules can help investors understand the power of compound interest. The higher the rate of return, the less time it takes to double or triple an investment.

How to use the rule of 72 to estimate returns
Let's say you have an investment balance of $ 100,000 and you want to know how long it will take you to get to $ 200,000 without adding more funds. With an estimated annual return of 7%, you would divide 72 by 7 to see that your investment will double every 10.29 years.

Here is an example of other rates of return and how the Rule of 72 affects your investment:

Rate of ReturnYears it Takes to Double
1%72
2%36
3%24
4%18
5%14.4
6%12
7%10.3
8%9
9%8
10%7.2
11%6.5
12%6

However, this simple calculation is not foolproof. If you have a little more time and want a more accurate result, you can use the following logarithmic formula:

T = ln (2) / ln (1 + r)

In this equation, "T" is the time for investment to double, "ln" is the natural logarithmic function, and "r" is the compound interest rate.

So to use this formula for the $ 100,000 investment mentioned above, with a 6% rate of return, you can determine that your money will double in 11.9 years, which is close to the 12 years you would get if you simply divided. 6

See what the logarithmic formula looks like in this case:

T = ln (2) / ln (1 + 0.06)

How to use the rule of 72 to estimate compound interest

Like most equations, you can move variables to solve those of which you are not sure. If you are looking back at an investment that you have held for several years and want to know what the annual compound interest yield was, you can divide 72 by the number of years it took for your investment to double.

For example, if you started with $ 100,000 and eight years later your balance is $ 200,000, divide 72 by 8 to get an annual rate of return of 9%.

Grain of salt

The rule of 72 is easy to calculate, but it is not always the correct approach. It requires a fixed rate of return to begin with, and while investors can use average stock market performance or other benchmarks, past performance does not guarantee future results. Therefore, it is important to do your research on expected rates of return and be conservative with your estimates.

Also, the simplest formula works best for rates of return between 6% and 10%. The Rule of 72 is not as accurate with rates on both sides of this range.

For example, with a rate of return of 9%, the simple calculation returns a time twice eight years. If you use the logarithmic formula, the answer is 8.04 years, a negligible difference.

Conversely, if you have a 2% rate of return, the Rule of 72 calculation returns a doubling time of 36 years. But if you calculate the numbers using the logarithmic formula, you are 35 years old, a difference of one full year.

As a result, if you just want a quick idea of ​​how long it will take for your investment to double, use the basic formula. But if you're calculating the amount as part of your retirement or education savings plan, consider using the logarithmic equation to make sure your assumptions are as accurate as possible.

Rule of 72 vs. 70

The Rule of 72 provides reasonably accurate estimates if your expected rate of return is between 6% and 10%. But if you're looking for lower fees, you might consider using the Rule of 70s.

For example, take our previous example of a 2% return. With the simple calculation of the Rule of 70, the time to double the investment is 35 years, exactly the same as the result of the logarithmic equation.

However, if you try to use it with a 10% return, the simple formula returns seven years, while the logarithmic function returns approximately 7.3 years, which has a larger discrepancy.

As with any general rule, the Rules of 72 and 70 are not perfect. But they can give you valuable information to help you with your long-term savings plan. Throughout this process, consider working with a financial advisor who can help you tailor an investment strategy to your situation.

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Source:Marko - WhiteBoard Finance

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