Rule of 70
What Is the Rule of 70?
The Rule of 70 is a simple way to determine how long it will take for an investment to double given a certain annual rate of return.
The rule states that you can divide the number 70 by the annual rate of return to get the approximate number of years it will take for your money to double.
For example, if you are earning a 7 percent annual rate of return on your investment, it will take approximately 10 years for your investment to double (70/7 = 10).
How Does the Rule of 70 Work?
The Rule of 70 is based on the power of compounding interest.
Compounding interest occurs when the interest earned on an investment is reinvested and begins to earn additional interest. This process can continue for years, resulting in exponential growth.
The Rule of 70 is a quick way to estimate the number of years it takes for an investment to double without having to do any complicated math.
How Is the Rule of 70 Derived?
The Rule of 70 is derived from the compound interest formula.
This formula states that the value of an investment will grow at a rate equal to the annual interest rate raised to the power of the number of years the investment is held.
For example, if you have an investment that earns a 7 percent annual return and you plan to hold it for 10 years, the future value of your investment can be calculated using the compound interest formula as follows:
FV = PV (1+r)^n
where:
- FV = future value of investment
- PV = present value of investment
- r = annual interest rate
- n = number of years invested
Substituting in the values from our example:
FV = $1,000 * (1 + 0.07) ^ 10
FV = $1,967.15
To calculate the number of years it will take for an investment to double using the compound interest formula, we can rearrange the equation as follows:
n = ln(FV/PV) / ln(1+r)
substituting in the values from our example:
n = ln($1,967.15/$1,000) / ln(1 + 0.07)
n = 9.999… or approximately 10 years
As can be observed, the compound interest formula produces a very similar result to the Rule of 70.
The Rule of 70 is a quick and easy way to estimate how long it will take for an investment to double, which can be helpful when planning for future goals.
However, it’s important to keep in mind that the rule is not exact and will produce slightly different results than the compound interest formula.
Why Is the Rule of 70 Important?
The Rule of 70 can be used as a tool to help you reach your financial goals. By understanding how long it will take for your money to double, you can develop a savings plan that allows you to reach your goals in a specific timeframe.
For example, if you know you can get 3.5 percent in real returns per year, then you know your investment will double (in inflation-adjusted terms) in 20 years.
The Rule of 70 can also be used as a way to compare investment options. The one with the shorter doubling time is the better investment, holding risk constant.
You can also use the Rule of 70 for reverse engineering what you need.
For example, if you want your investment to double every 10 years, you know you need 7 percent per year to achieve your goal. That could pertain to a standard passive investment, such as a stock or bond, or a personal project.
The Rule of 70 can be a helpful tool in personal finance, but it’s important to remember that it’s only an estimate. In reality, investments can take longer or shorter than predicted to double.
Investors should also keep in mind that the Rule of 70 doesn’t account for inflation on its own. Over time, inflation can reduce the purchasing power of your money, even if your investment is growing at a healthy rate.
For example, let’s say you have $10,000 invested at a 7 percent annual rate of return. In 10 years, your investment will be worth approximately $20,000.
However, if inflation is 3 percent per year, the purchasing power of your $20,000 will be equivalent to $14,802 today based on a real return of four percent per year.
Real returns are what are most important over time as the idea of an investment is to preserve or grow the purchasing power of money, not simply grow money itself.
Rule of 70 and Inflation
The rule of 70 can also be applied to other phenomena like inflation.
For example, if inflation is 3 percent, you can calculate how many years it would take of 3 percent inflation for the price level for goods and services (as an average) to double.
This would be about 23 years, taking 70 divided by 3 (23.33).
It is also commonly used for things in other fields, such as population doubling time.
Rule of 70 – FAQs
What is the Rule of 70?
The Rule of 70 is a quick and easy way to estimate how long it will take for an investment to double.
How is the Rule of 70 calculated?
To calculate the number of years it will take for an investment to double using the Rule of 70, divide the number 70 by the annual rate of return.
What are some limitations of the Rule of 70?
The Rule of 70 is only an estimate and will produce slightly different results than the compound interest formula.
How can I use the Rule of 70 to reach my financial goals?
By understanding how long it will take for your money to double, you can develop a savings plan that allows you to reach your goals in a specific timeframe.
What is the difference between the Rule of 70 and the compound interest formula?
The Rule of 70 is a quick and easy way to estimate how long it will take for an investment to double, while the compound interest formula is more exact.
How can I account for inflation when using the Rule of 70?
Inflation can reduce the purchasing power of your money, even if your investment is growing in dollar terms.
To account for inflation, use a real rate of return rather than a nominal rate of return.
How is the Rule of 70 different from the Rule of 72?
The Rule of 72 is a similar calculation, but it uses the number 72 instead of 70, mostly because the mental math is easier (more numbers will evenly divide when using the Rule of 72 vs. the Rule of 70).
The Rule of 72 will produce slightly different results than the Rule of 70, but they will be close.
What is the history of the Rule of 70?
The Rule of 70 has been used by economists and mathematicians for centuries as a way to estimate exponential growth.
A similar calculation, known as the Rule of 72, has been used since the 18th century.
Summary – Rule of 70
The Rule of 70 is a quick and easy way to estimate how long it will take for an investment to double.
To calculate the number of years it will take for an investment to double using the Rule of 70, divide the number 70 by the annual rate of return.
The Rule of 70 is only an estimate and will produce slightly different results than the compound interest formula.
By understanding how long it will take for your money to double, you can develop a savings plan that allows you to reach your goals in a certain timeframe.
Inflation can reduce the purchasing power of your money, so to account for inflation, it can be a good idea to use a real rate of return rather than a nominal rate of return.
The Rule of 72 is a similar rule, but it uses the number 72 in the numerator instead of 70, largely as a way of simplifying the mental math related to the calculations, as 72 can easily divide by 3, 4, 6, 8, 9, and 12 while 70 does not.