If you’ve ever wanted to convince someone else or yourself about the power of compounding – and why you should begin investing today – then the “Rule of 72” is a useful rule of thumb to depict its benefits.
The “Rule of 72” is a simple way to estimate how many years it takes for your investments to double, compounded at a fixed annual rate of return. To enjoy the effect of compounding, you must also reinvest your yearly returns and strive to receive the same annual rate of return each year.
What Does the “Rule of 72” Say?
Remember that this rule of thumb is not a substitute for proper calculations, which typically require a scientific calculator and a good understanding of logarithms. That being said, it is a really handy tool to quickly derive a relatively accurate estimate for how long it takes to double your investments.
Here’s the “Rule of 72” formula:
Years required to double your investments = 72 / Compound Annual Interest Rate (CAGR)
Simple? For example, the CPF Special Account currently gives 4% in interest per annum. Thus, using the “Rule of 72”, it will take 72/4 = 18 years for our monies to double. The actual number of years is 17.67, which shows the “Rule of 72” is pretty close.
If you are able to achieve a higher rate of return, even by a few percentage points, you will drastically shorten the amount of years required to double your investments. Similarly, if you receive a lower rate of return each year, you may take a much longer time to double your investments.
Here is a table of annual compounded interest rates, and what the “Rule of 72” gives, compared to the actual number of years:
| Compound Annual Interest Rate (CAGR) | Number of Years to Double (Rule of 72) | Actual Number of Years to Double |
|---|---|---|
| 1% | 72 | 69.66 |
| 2% | 36 | 35 |
| 3% | 24 | 23.45 |
| 4% | 18 | 17.67 |
| 5% | 14.4 | 14.21 |
| 6% | 12 | 11.9 |
| 7% | 10.29 | 10.24 |
| 8% | 9 | 9.01 |
| 9% | 8 | 8.04 |
| 10% | 7.2 | 7.27 |
In general, the “Rule of 72” gets you quite close to the actual figures, though it may become pretty inaccurate once interest rates are at 20% and higher. If you’re able to achieve such interest returns on an annual basis over a long period of time, it’s safe to assume you will be able to derive such complicated calculations on your own.
Applications of the Rule of 72
The Rule of 72 could apply to anything that grows at a compounded rate, such as population, GDP growth, and even inflation, investment returns, or fees.
For most, returns and fees are important figures you may want to calculate before making an investment. You can use the table above to estimate how long your investments will take to double, and how long more you need if you factor in annual investment fees.
The rule can also be used to find the amount of time it takes for your money’s value to halve due to inflation. If inflation is 6%, then a given purchasing power of the money will be worth half in around (72 ÷ 6) = 12 years. If inflation decreases from 6% to 4%, an investment will be expected to lose half its value in 18 years, instead of 12 years. This is also another important reason to invest and to receive an investment return that beats the inflation rate.
What Can the “Rule of 72” Teach Us?
The Rule of 72 depicts how even a “small” 1% difference in inflation, fees, or investment return can have a large effect in forecasting models. If you wish to double your money, receiving a single percent less can extend the number of years you need to reach your goal.
This also highlights the importance of carefully evaluating the potential returns of each investment product, after accounting for fees and costs. These differences can add up significantly over the long run and have a big impact on your retirement plans.
Secondly, the rule elegantly illustrates the “magical” power of compounding. If you diligently invest and receive even a modest rate of return (4% to 5%), you can actually double your initial capital in less than two decades.
In order to allow this compounding to work, all that’s needed is time and diligence. By planning for one’s retirement early and starting to invest today, you can ensure you’re growing your retirement nest egg so that it will be ready for your retirement needs in your golden years.
Someone who starts investing only in their forties may need to contribute many times more money to their retirement funds but will still not have a larger retirement nest egg compared to someone else who started in their thirties or even twenties. This is because they were not able to leverage time to compound their investments.
Practical Applications of the Rule of 72
Estimating Investment Growth
The primary use of the Rule of 72 is to estimate how long it will take for an investment to double. This can be particularly useful for comparing different investment options. For instance, if you’re deciding between two investments with different expected rates of return, you can use the Rule of 72 to see which one will double your money faster.
Assessing the Impact of Fees
Investment fees can significantly affect your returns over time. By factoring in fees, you can use the Rule of 72 to understand how they impact the time it takes for your investment to double. For example, if an investment has a 7% return but a 1% annual fee, your effective return is 6%, meaning it will take 12 years to double instead of about 10 years without the fee.
Understanding Inflation
The Rule of 72 can also be applied to inflation. If the inflation rate is 3%, the purchasing power of your money will halve in about 24 years (72 ÷ 3 = 24). This highlights the importance of earning a return that outpaces inflation to preserve and grow your purchasing power.
Limitations of the Rule of 72
While the Rule of 72 is a useful approximation, it is not precise. It provides a close estimate for interest rates that are not too high. For very high rates of return (e.g., 20% or more), the rule becomes less accurate. Additionally, the Rule of 72 assumes a fixed annual rate of return, which is not always realistic in the volatile world of investments.
Benefits of Using the Rule of 72
Simplifies Complex Calculations
The Rule of 72 simplifies the complex mathematics of compound interest, allowing even those with minimal financial expertise to make quick estimates about their investments.
Aids in Financial Planning
By providing a quick estimate of how long it will take for investments to grow, the Rule of 72 can help investors set realistic goals and timelines for their financial objectives.
Encourages Early Investing
Understanding the power of compounding and how quickly investments can grow when given enough time can motivate individuals to start investing early, maximizing their long-term returns.
The Rule of 72 is a powerful and simple tool that can help you understand the potential growth of your investments. By providing a quick estimate of the time required to double your money, it aids in making informed investment decisions and highlights the importance of starting early and maintaining consistent returns. While it is not a substitute for detailed financial analysis, the Rule of 72 is a valuable addition to any investor’s toolkit, helping to demystify the process of wealth accumulation through compounding.
