Have you ever pondered how long it might take for your money to double with interest? The Rule of 72 offers a straightforward technique to provide a rough estimate.
Understanding the Rule of 72
Here’s how it operates: Divide 72 by your anticipated annual interest rate (as a percentage, not a decimal). The result will give you an approximate number of years required for your money to double.
For instance, if your investment yields 4 percent per annum, it would take around 72 / 4 = 18 years to double.
This principle can also be applied to inflation. Just as with investment growth, divide 72 by the inflation rate (again, as a percentage) to estimate the time it will take for your money’s purchasing power to halve.
The Rule of 72 serves as an estimation tool and is most accurate at approximately 8 percent interest. The further the interest rate or inflation rate deviates from 8 percent, the less precise the outcome will be.
Despite its limitations, the Rule of 72 proves to be a useful tool for gaining a quick insight into how your money may grow over time, based on a specific interest rate.
The formula for the Rule of 72
The Rule of 72 can be succinctly expressed as:
Years to double = 72 / rate of return on investment (or interest rate)
There are a few crucial points to note with this formula:
- The interest rate should not be represented as a decimal out of 1, such as 0.07 for 7 percent. It should simply be the number 7. Therefore, 72/7 equals 10.3, or 10.3 years.
- The Rule of 72 pertains to compounding interest that compounds annually.
- For simple interest, you would divide 1 by the interest rate expressed as a decimal. For instance, if you had $100 with a 10 percent simple interest rate without compounding, you would divide 1 by 0.1, resulting in a doubling rate of 10 years.
- For continuous compounding interest, using 69.3 instead of 72 yields more accurate results. The Rule of 72 is an approximation, and 69.3 provides slightly more accurate results than 72. If you have access to a calculator, use 69.3 for increased precision.
- The further you deviate from an 8 percent return, the less accurate your outcomes will be. The Rule of 72 functions optimally within the 5 to 10 percent range, but it remains an approximation. To calculate based on a lower interest rate, like 2 percent, adjust the 72 to 71. For calculating based on a higher interest rate, such as 16 percent, increment the value by one for every 3 percentage point increase. Consequently, use 74 for determining doubling time with 16 percent interest.
Understanding the Functionality of the Rule of 72
The actual mathematical formula is intricate and derives the number of years until doubling based on the time value of money.
Commence with the future value calculation for periodic compounding rates of return, a calculation that aids individuals interested in computing exponential growth or decay. FV represents future value, PV denotes present value, r signifies the rate, and t indicates the time period.
FV = PV*(1+r)t
To isolate t when it’s located within an exponent, you can leverage natural logarithms of both sides. Natural logarithms serve as a mathematical approach to solving for an exponent. A natural logarithm of a number corresponds to the number’s own logarithm to the power of e, an irrational mathematical constant approximately equal to 2.718. When considering the illustration of doubling $10, deriving the Rule of 72 would proceed as follows:
20 = 10*(1+r)t
20/10 = 10*(1+r)t/10
2 = (1+r)t
ln(2) = ln((1+r)t)
ln(2) = r*t
The natural logarithm of 2 amounts to 0.693147, hence when you solve for t utilizing those natural logarithms, you obtain t = 0.693147/r.
The actual outcomes are not whole numbers and are closer to 69.3, yet 72 conveniently divides for numerous common rates of return that individuals receive on their investments. Therefore, 72 has gained popularity as a value for estimating doubling time.
For more precise insights into how your investments are likely to progress, utilize a compound interest calculator founded on the complete formula.
Employing the Rule of 72 for Investment Planning
Many families aspire to sustain investing over time, frequently on a monthly basis. You can forecast the duration required for your compound interest investment to reach a specified target amount if you possess an average rate of return and a current balance.
For instance, if you currently have $100,000 invested at 10 percent interest and are 22 years away from retirement, you can anticipate your money doubling approximately three times, escalating from $100,000 to $200,000, then to $400,000, and ultimately reaching $800,000.
If your interest rate fluctuates or you necessitate additional funds due to inflation or other factors, leverage the outcomes from the Rule of 72 to guide your decisions on how to persistently invest over time.
You can also utilize the Rule of 72 to make informed choices regarding risk versus reward. For instance, if you possess a low-risk investment generating 2 percent interest, you can compare the doubling rate of 36 years to that of a high-risk investment yielding 10 percent and doubling in seven years.
Youthful adults frequently gravitate towards higher-risk investments owing to the potential for exponential growth. With an extended time horizon, they can endure market fluctuations and potentially benefit from multiple periods of doubling their money. Consequently, stocks are regarded as one of the prime investments for college students and other young adults.
Nonetheless, as individuals approach retirement, their investment strategy typically transforms. The emphasis shifts from high returns to capital preservation. Given their narrowing time frame, doubling their money becomes less pivotal. Instead, they prioritize the security of their nest egg by opting for lower-risk investments. This ensures they secure a predictable and stable income source in their later years.
Applying the Rule of 72 to Inflation
Investors can leverage the Rule of 72 to ascertain the duration required to diminish their purchasing power by half due to inflation. For instance, with inflation currently hovering around 3 percent, dividing 72 by the inflation rate reveals 24 years until your money’s purchasing power is cut in half. Nevertheless, high inflation, exemplified by the 8 percent rate prevalent in 2023, accelerates the halving of purchasing power to nine years.
72/3 = 24 years to lose half your purchasing power
72/8 = 9 years
The Rule of 72 enables investors to comprehend the tangible impact of inflation. While inflation may not consistently remain elevated, historical data showcases periods when it endured for years, substantially eroding the purchasing power of savings.
Conclusion
The Rule of 72 serves as a valuable tool for individuals embarking on their investment journey. It underscores the significance of early investing, even with modest sums. The power of compounding interest facilitates the exponential growth of your money over time, particularly when you make substantial initial investments. Additionally, you can utilize the Rule of 72 to grasp the repercussions of inflation. By dividing 72 by the inflation rate, you can estimate the duration until your money’s purchasing power diminishes by half.
Note: Laura Leavitt contributed to this story.