Here’s the formula:
Years to double = 72 / Interest Rate
This formula is useful for financial estimates and understanding the nature of compound interest.
Years to double = 72 / Interest Rate
This formula is useful for financial estimates and understanding the nature of compound interest.
Examples:
You can also use the rule of 72 for expenses like inflation or interest:
The rule of 72 shows why a “small” 1% difference in inflation or GDP expansion has a huge effect in forecasting models.
By the way, the Rule of 72 applies to anything that grows, including population. Can you see why a population growth rate of 3% vs 2% could be a huge problem for planning? Instead of needing to double your capacity in 36 years, you only have 24. Twelve years were shaved off your schedule with one percentage point.
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IN INVESTMENT
WHAT IT IS:
The "rule of 72" is a method of estimating how long it will take compounding interest to double an investment.
HOW IT WORKS (EXAMPLE):
The rule of 72 is a method used in finance to quickly estimate the doubling or halving time through compound interest or inflation, respectively.
For example, using the rule of 72, an investor who invests $1,000 at an interest rate of 4% per year, will double their money in approximately 18 years.
72 / [periodic interest rate] = [number of years to double principal]
or
72 / 4 = 18
Using the same rule of 72, an investor who invests $1000 with an annual inflation rate of 2% will lose half of their principal in 36 years.
72 / 2 = 36
The rule of 72 can also be used to demonstrate the long term effects of period fees on an investment, such as a mutual funds, life insurance, and private equity funds. For example, not counting any appreciation of the underlying investments in the fund, a mutual fund with a 3% annual loading and expense fee on principal invested will cut the principal in half over 24 years.
72/ 3 = 24
The rule of 72 is an approximation. It is not exact. Indeed, the rule of 72 is accompanied by the rule of 70, and the rule of 69 which are used the same way, but are more accurate for smaller periodic interest rates. The rule of 72 is popular because it is divisible for more numbers (i.e. possible interest rates).
WHY IT MATTERS:
While this calculation is relatively simple with a calculator or spreadsheet, the rule of 72, which was derived before the 14th century, is still a quick, mental calculation for the effects of compound interest.
- At 6% interest, your money takes 72/6 or 12 years to double.
- To double your money in 10 years, get an interest rate of 72/10 or 7.2%.
- If your country’s GDP grows at 3% a year, the economy doubles in 72/3 or 24 years.
- If your growth slips to 2%, it will double in 36 years. If growth increases to 4%, the economy doubles in 18 years. Given the speed at which technology develops, shaving years off your growth time could be very important.
You can also use the rule of 72 for expenses like inflation or interest:
- If inflation rates go from 2% to 3%, your money will lose half its value in 24 years instead of 36.
- If college tuition increases at 5% per year (which is faster than inflation), tuition costs will double in 72/5 or about 14.4 years. If you pay 15% interest on your credit cards, the amount you owe will double in only 72/15 or 4.8 years!
The rule of 72 shows why a “small” 1% difference in inflation or GDP expansion has a huge effect in forecasting models.
By the way, the Rule of 72 applies to anything that grows, including population. Can you see why a population growth rate of 3% vs 2% could be a huge problem for planning? Instead of needing to double your capacity in 36 years, you only have 24. Twelve years were shaved off your schedule with one percentage point.
--------------------------------------------------------------------------
IN INVESTMENT
WHAT IT IS:
The "rule of 72" is a method of estimating how long it will take compounding interest to double an investment.
HOW IT WORKS (EXAMPLE):
The rule of 72 is a method used in finance to quickly estimate the doubling or halving time through compound interest or inflation, respectively.
For example, using the rule of 72, an investor who invests $1,000 at an interest rate of 4% per year, will double their money in approximately 18 years.
72 / [periodic interest rate] = [number of years to double principal]
or
72 / 4 = 18
Using the same rule of 72, an investor who invests $1000 with an annual inflation rate of 2% will lose half of their principal in 36 years.
72 / 2 = 36
The rule of 72 can also be used to demonstrate the long term effects of period fees on an investment, such as a mutual funds, life insurance, and private equity funds. For example, not counting any appreciation of the underlying investments in the fund, a mutual fund with a 3% annual loading and expense fee on principal invested will cut the principal in half over 24 years.
72/ 3 = 24
The rule of 72 is an approximation. It is not exact. Indeed, the rule of 72 is accompanied by the rule of 70, and the rule of 69 which are used the same way, but are more accurate for smaller periodic interest rates. The rule of 72 is popular because it is divisible for more numbers (i.e. possible interest rates).
WHY IT MATTERS:
While this calculation is relatively simple with a calculator or spreadsheet, the rule of 72, which was derived before the 14th century, is still a quick, mental calculation for the effects of compound interest.
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