Have you ever found it challenging to understand interest rates or the rate of return on an investment, or grasp the concept of compounding? Having a quick way to estimate investment growth can be incredibly useful. This is where the Rule of 72 comes in.
It’s a straightforward yet powerful financial formula that helps investors estimate the time it will take for an investment to double in value. Whether you’re planning for retirement, saving for a significant purchase, or simply aiming to grow your wealth, understanding and applying the Rule of 72 can offer valuable insights into your financial future.
What is the Rule of 72?
A bit of history about the Rule of 72: it can be traced back to 1494 when Luca Pacioli mentioned it in his mathematics book Summa de Arithmetica. However, Pacioli did not provide any derivation or explanation for the rule’s effectiveness, leading some to believe that it predates his work. At its core, the Rule of 72 is a straightforward formula used to estimate the number of years it will take for an investment to double at a fixed annual rate of return. The basic formula is:
Years to double = 72 ÷ Annual rate of return
For instance, if you have an investment earning 6% annually, it would take approximately 12 years to double (72 ÷ 6 = 12). It’s worth noting that while the Rule of 72 isn’t exact but it provides a remarkably accurate approximation for most practical purposes, especially for interest rates between 6% and 10%. If you want to determine the exact doubling time for an investment earning a compounded interest rate of r% per period, the formula is:
t = ln(2)/ln[1+(r/100)]
Where:
- t is the time in periods for the investment to double
- r is the annual rate of return (expressed as a percentage)
- ln denotes the natural logarithm
As we can see, the original formula is long and complex, while the Rule of 72 is short and easy to calculate mentally.
Practical applications
Now that we understand the Rule of 72, let’s explore how it can be applied. This versatile tool offers several valuable applications for investors. Here are some examples:
1. Estimating investment growth. Since the Rule of 72 allows you to quickly calculate how long it will take for your investments to double, it provides insights that can help you set more realistic financial goals and make informed decisions about your investment strategy.
For example, with an average stock market return of 7% after inflation, we can estimate that an investment in a broad market index fund would double in about 10.3 years (72 ÷ 7 = 10.3). This is particularly useful when planning for your retirement savings.
2. Comparing different investment options. When faced with various investment opportunities, the Rule of 72 allows you to easily compare their potential growth rates. For instance, imagine you’re deciding between two investments: a conservative bond offering 3% annual returns and a more aggressive stock fund promising 9% returns. Simply looking at the rates might not reveal the impact of time based on your returns.
But with the Rule of 72, you can quickly determine that the bond fund would take about 24 years to double your money (72 ÷ 3 = 24), while the stock fund would take only 8 years (72 ÷ 9 = 8). This comparison clearly illustrates the difference and can help you make informed decisions based on your financial goals and risk tolerance.
3. Understanding the impact of fees. Fees can significantly affect your investment returns over time; even a 1% fee can substantially alter the years it takes for an investment to double. Applying the Rule of 72 to the difference between growth returns and returns after fees lets you visualize how fees impact long-term growth.
Let’s say you’re considering two similar funds with slight differences in fees: Fund A (7% return and 0.5% fee) and Fund B (7% return and 1% fee). After fees, we can expect Fund A to have a return of 6.5% (doubling in 11.1 years) and Fund B to have a return of 6% (doubling in 12 years). Over several decades, this seemingly small difference can amount to many thousands of dollars and significantly eat into your profits.
4. Measuring the effects of inflation. As we all know, inflation erodes the purchasing power of money over time. You can use the Rule of 72 to estimate how quickly the value of your money will halve due to inflation. For instance, if we assume an average inflation rate of 2% per year, the Rule of 72 tells us that the purchasing power of money would halve in just 36 years (72 ÷ 2 = 36).
This underscores the importance of investing as early as possible to outpace inflation. It also explains why keeping all your money in a bank with a zero or low-yield savings account may not be the best long-term strategy. While it would take 72 years for your savings to double at 1% interest, inflation would have halved its value in just 36 years.
What are its limitations?
While the Rule of 72 is undoubtedly useful, it’s essential to understand its limitations. Firstly, the rule assumes a constant growth rate, which isn’t always realistic in the volatile world of investments. Secondly, it doesn’t account for more frequent compounding periods, which can affect the estimate’s accuracy. Thirdly, the rule’s accuracy varies with interest rates. As mentioned, it’s most precise for rates ranging between 6% and 10%. Outside this range, the approximation becomes less accurate.
To address one of these limitations and improve accuracy, we can adjust the Rule of 72 accordingly. Remember, the Rule of 72 works best at an 8% interest rate (or between 6% to 10%). For every three points that an interest rate strays from 8%, you can adjust the ‘72’ by one in the direction of the rate change.
For example, if the rate is 5%, you would lower the rule to 71; if the rate is 11%, you would adjust it to 73. This is where the variations, Rule of 71 and Rule of 73, come from. However, for most everyday calculations, the standard Rule of 72 remains sufficiently accurate and easier to remember.
The fifth perspective
In short, the Rule of 72 is a simple yet powerful tool that can quickly and effectively provide valuable insights into investment growth. By understanding and applying this rule, you can make more informed decisions about your financial future, set realistic goals, and better evaluate investment opportunities.
