Even if you are familiar with the rule, can you tell (without using a pen or calculator) which product has the highest interest rate?
- Product A doubles in 8 years
- Product B triples in 14 years
- Product C quadruples in 18 years
In this article, we explain the Rule of 72 and other shortcuts which will help you find out the answer to this question.
Rule of 72
This shortcut helps approximate the time or growth rate needed for something to double when compounded annually. If you want to know the interest rate, divide 72 by the number of years.
Interest Rate = 72 ÷ Number of years
Likewise, if you want to know the number of years, divide by 72 by ROI.
Number of years = 72 ÷ Interest Rate
Example 1
If you want to double your investment in 12 years, what return should you require?
Interest Rate = 72 ÷ Number of years
= 72 ÷ 12 years
= 6%
Example 1
If your investment is growing at 9%, how many years will it take to double?
Number of years = 72 ÷ Interest Rate
= 72 ÷ 9%
= 8 years
When you want money to grow 3x, 4x, and 5x
For such mental calculations, the formula is the same but the factor is different.
Growth of Investment | Factor to use |
| 2x (double) | 72 |
| 3x (triple) | 114 |
| 4x (quadruple) | 144 |
| 5x | 167 |
Which fetches the highest return?
Returning to our original problem, Product A fetches the highest return on investment. Here’s why.
Product A which doubles in 8 years
= 72 ÷ Number of years = 72 ÷ 8 = 9%
Product B triples in 14 years
= 114 ÷ Number of years = 114 ÷ 14 = 8% (approximately)
Product C quadruples in 18 years.
= 144 ÷ Number of years = 144 ÷ 18 = 8%
Things to remember
- Although the Rule of 72 is a good approximation, it never gives an exact answer. For an exact answer, please use a pen and paper, or calculator.
- It is most accurate for only for a certain range of interest rates or number of years. For interest rates or number of years from 3 to 20, the Rule of 72 has an accuracy of more than 90%. Please click here to see its accuracy from 1 to 25 for interest rates and number of years.
- As most investment periods and ROI of most products fall in this range, the Rule of 72 is good enough for most investing situations. For example, most products deliver a return of 3% to 17% and most investment horizons are between 3 years and 20 years.
- 72 is most commonly used because it is divisible by many numbers. In case of daily compounding, the Rule of 70 or Rule of 69.3 is used.
- This rule can be used for anything which grows or reduces in a compounded manner. For example, if a population is shrinking by 1.8% annually, it will approximately take 40 years (72 ÷ 1.8) to reduce by half. Likewise, it will take approximately 63 years (114 ÷ 1.8) to get reduced to one-third.
- To give another example, suppose your portfolio generates a return of 4% after taxes even as your personal inflation rate (yes, this may be different from the official inflation rate) stands at 7.6%. In other words, your portfolio is effectively depreciating by 3.6% per annum. Applying the same rule, in 20 years (72 ÷ 3.6), your money will be reduced to half its purchasing power.
Accuracy of Rule of 72
ROI reqd. for Doubling | Time reqd. for Doubling | ||||||
No. of Years is given | Approx. rate using Rule of 72 | Actual Rate | Accuracy | Interest Rate is given | Approx. no. of years using Rule of 72 | Actual Years | Accuracy |
1 | 72 | 100 | 72.00% | 1 | 72 | 69.66 | 96.75% |
2 | 36 | 41.42 | 86.91% | 2 | 36 | 35 | 97.22% |
3 | 24 | 25.99 | 92.34% | 3 | 24 | 23.45 | 97.71% |
4 | 18 | 18.92 | 95.14% | 4 | 18 | 17.67 | 98.17% |
5 | 14.4 | 14.87 | 96.84% | 5 | 14.4 | 14.21 | 98.68% |
6 | 12 | 12.25 | 97.96% | 6 | 12 | 11.9 | 99.17% |
7 | 10.29 | 10.41 | 98.81% | 7 | 10.29 | 10.24 | 99.56% |
8 | 9 | 9.05 | 99.45% | 8 | 9 | 9.01 | 99.89% |
9 | 8 | 8.01 | 99.88% | 9 | 8 | 8.04 | 99.50% |
10 | 7.2 | 7.18 | 99.72% | 10 | 7.2 | 7.27 | 99.04% |
11 | 6.55 | 6.5 | 99.31% | 11 | 6.55 | 6.64 | 98.58% |
12 | 6 | 5.95 | 99.17% | 12 | 6 | 6.12 | 98.04% |
13 | 5.54 | 5.48 | 98.94% | 13 | 5.54 | 5.67 | 97.68% |
14 | 5.14 | 5.08 | 98.78% | 14 | 5.14 | 5.29 | 97.22% |
15 | 4.8 | 4.73 | 98.54% | 15 | 4.8 | 4.96 | 96.77% |
16 | 4.5 | 4.43 | 98.44% | 16 | 4.5 | 4.67 | 96.36% |
17 | 4.24 | 4.16 | 98.22% | 17 | 4.24 | 4.41 | 96.04% |
18 | 4 | 3.93 | 98.25% | 18 | 4 | 4.19 | 95.47% |
19 | 3.79 | 3.72 | 98.17% | 19 | 3.79 | 3.98 | 95.21% |
20 | 3.6 | 3.53 | 98.06% | 20 | 3.6 | 3.8 | 94.74% |
21 | 3.43 | 3.36 | 98.00% | 21 | 3.43 | 3.64 | 94.19% |
22 | 3.27 | 3.2 | 97.78% | 22 | 3.27 | 3.49 | 93.77% |
23 | 3.13 | 3.06 | 97.75% | 23 | 3.13 | 3.35 | 93.45% |
24 | 3 | 2.93 | 97.67% | 24 | 3 | 3.22 | 93.17% |
25 | 2.88 | 2.81 | 97.57% | 25 | 2.88 | 3.11 | 92.60% |
