what is the rule of 72?
The rule of 72 is a calculation that estimates the number of years it takes to double your money at a specific rate of return. If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. in this case, 18 years.
The same calculation can also be useful for inflation, but it will reflect the number of years until the initial value has been halved, rather than doubled.
The rule of 72 is derived from a more complex calculation and is an approximation, so it is not perfectly accurate. the most accurate rule of 72 results are based on the 8 percent interest rate, and the farther you go from 8 percent in either direction, the less accurate the results will be. Still, this handy formula can help you better understand how much your money can grow, assuming a specific rate of return.
the rule of 72 formula
The rule of 72 can be expressed simply as:
years to double = 72 / rate of return on investment (or interest rate)
There are some important caveats to understand with this formula:
- The interest rate should not be expressed as a decimal of 1, such as 0.07 for 7 percent. it should just be the number 7. So, for example, 72/7 is 10.3 or 10.3 years.
- The rule of 72 focuses on compound interest compounded annually.
- for simple interest, simply divide 1 by the interest rate expressed as a decimal. If you had $100 at a 10 percent simple interest rate with no compounding, you would divide 1 by 0.1, which would give you a 10-year doubling rate.
- for continuous compound interest, you will get more accurate results if you use 69.3 instead of 72. the rule of 72 is an estimate, and 69.3 is more difficult for mental math than 72, which is easily divided by 2, 3, 4, 6, 8, 9, and 12. However, if you have a calculator, use 69.3 to get slightly more precise results.
- The further away you are from an 8 percent return, the less accurate your results will be. the rule of 72 works best in the 5 to 12 percent range, but it’s still an approximation.
- To calculate based on a lower interest rate, such as 2 percent, reduce 72 to 71; to calculate based on a higher interest rate, add one to 72 for every three percentage point increase. so, for example, use 74 if you’re calculating the doubling time for 18 percent interest.
how the rule of 72 works
The actual mathematical formula is complex and derives the number of years until it doubles based on the time value of money.
I would start with calculating the future value for periodic compounding rates of return, a calculation that helps anyone interested in calculating exponential growth or decay:
fv = pv*(1+r)t
fv is the future value, pv is the present value, r is the rate, and t is the time period. to isolate t when it is in an exponent, you can take the natural logarithms of both sides. Natural logarithms are a mathematical way of solving for an exponent. a natural logarithm of a number is the logarithm of the number raised to e, an irrational mathematical constant that is approximately 2.718. Using the example of a doubling of $10, deriving the rule of 72 would look like this:
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 log of 2 is 0.693147, so when you solve for t using those natural logs, you get t = 0.693147/r.
Actual results are not round numbers and are closer to 69.3, but 72 breaks down easily for many of the common rates of return people earn on their investments, which is why 72 has gained popularity as a value for estimate the doubling time.
For more accurate data on how your investments are likely to grow, use a compound interest calculator based on the full formula.
how to use the rule of 72 for investment planning
Most families intend to continue investing over time, often monthly. You can project how long it will take to reach a given target amount if you have an average rate of return and a current balance. If, for example, you have $100,000 invested today at 10 percent interest and you are 22 years from retirement, you can expect your money to double about three times, going from $100,000 to $200,000, then to $400,000, and then to $800,000.
If your interest rate changes or you need more money due to inflation or other factors, use the results of the rule of 72 to help you decide how to keep investing over time.
You can also use the rule of 72 to choose between risk and reward. If, for example, you have a low-risk investment that pays 2 percent interest, you can compare the doubling rate over 36 years with that of a high-risk investment that pays 10 percent and doubles in seven years.
Many young adults just starting out choose high-risk investments because they have the opportunity to take advantage of high rates of return for multiple doubling cycles. Those approaching retirement, however, will likely choose to invest in lower-risk accounts as they get closer to their retirement target amount because doubling down is less important than investing in safer investments.
rule of 72 during inflation
investors can use the rule of 72 to see how many years it will take for their purchasing power to be halved due to inflation. For example, if inflation is running around 8 percent (as in mid-2022), you can divide 72 by the inflation rate to get 9 years until the purchasing power of your money drops by 50 percent.
72/8 = 9 years to lose half of your purchasing power.
The rule of 72 allows investors to realize the seriousness of inflation in a concrete way. Inflation may not stay elevated for such a long period of time, but it has in the past over a period of several years, which really hurt the purchasing power of accumulated assets.
end result
The rule of 72 is an important guideline to keep in mind when considering how much to invest. Investing even a small amount can have a big impact if you start early, and the effect can only increase the more you invest, as the power of compounding works its magic. You can also use the rule of 72 to assess how quickly you can lose purchasing power during periods of inflation.
note: georgina tzanetos from bankrate contributed to a recent update to this story.
