Loading the player...

What is the 'Rule Of 72'

The rule of 72 is a shortcut to estimate the number of years required to double your money at a given annual rate of return. The rule states that you divide the rate, expressed as a percentage, into 72:

Years required to double investment = 72 ÷ compound annual interest rate

Note that a compound annual return of 8% is plugged into this equation as 8, not 0.08, giving a result of 9 years (not 900).

BREAKING DOWN 'Rule Of 72'

The rule of 72 is a useful shortcut, since the equations related to compound interest are too complicated for most people to do without a calculator. To find out exactly how long it would take to double an investment that returns 8% annually, one would have to use this equation:

T = ln(2) / ln(1.08) = 9.006

Most people cannot do logarithmic functions in their heads, but they can do 72 ÷ 8 and get almost the same result. If it takes 9 years to double a $1,000 investment, then the investment will grow to $2,000 in Year 9, $4,000 in Year 18, $8,000 in Year 27, and so on. Conveniently, 72 is divisible by 2, 3, 4, 6, 8, 9, and 12, making the calculation even simpler.

The unit does not necessarily have to be money: the rule could apply to any thing that grows, such as population. If Gross Domestic Product (GDP) grows at 4% annually, the economy will be expected to double in 72 ÷ 4 = 18 years. Also, in regards to fees that cut into investment gains, the rule of 72 can be used to demonstrate the long-term effects of these costs. A mutual fund that has 3% in annual expense fees will cut the investment principal in half over 24 years. A borrower that pays 12% interest on his credit cards will double the amount he owes in 6 years.

The rule can also be used to find the amount of time it takes for money's value to halve due to inflation. If inflation is 6%, then a given amount of money will be worth half as much in 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.

Adjusting For Higher Rates

The rule of 72 is reasonably accurate for interest rates between 6% and 10%. When dealing with rates outside this range, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate diverges from 8%. So for 11% annual compounding interest, the rule of 73 is more appropriate; for 14%, it would be the rule of 74; for 5%, the rule of 71.

For example, say you have a 22% rate of return (congratulations). The rule of 72 says the initial investment will double in 3.27 years. Since 22 – 8 is 14, and 14 ÷ 3 is 4.67 ≈ 5, the adjusted rule would use 72 + 5 = 77 for the numerator. This gives a return of 3.5, meaning you'll have to wait another quarter to double your money. The period given by the logarithmic equation is 3.49, so the adjusted rule is more accurate.

Adjusting For Continuous Compounding

For daily or continuous compounding, using 69.3 in the numerator gives a more accurate result. Some people adjust this to 69 or 70 for simplicity sake. 

 

RELATED TERMS
  1. Rule Of 70

    The rule of 70 is a means of estimating the number of years it ...
  2. Future Value - FV

    Future value (FV) is the value of a current asset at a date to ...
  3. Compounding

    Compounding is the process in which an asset's earnings, from ...
  4. 25% Rule

    The 25% rule is the idea that a local government's long-term ...
  5. Interest Rate

    Interest rate is the amount charged, expressed as a percentage ...
  6. Call Rule

    The call rule is a rule for trading markets that makes the next ...
Related Articles
  1. Investing

    How To Double Your Money Every 6 Years

    Investing according to the rule of 72 is a good starting point for achieving your saving goals.
  2. Investing

    Understanding the Power of Compound Interest

    Understanding compound interest is important for both investing and borrowing money.
  3. Investing

    Overcoming Compounding's Dark Side

    Understanding how money is made and lost over time can help you improve your returns.
  4. Investing

    The Effective Annual Interest Rate

    The effective annual interest rate is a way of restating the annual interest rate so that it takes into account the effects of compounding.
  5. Investing

    5 Top Ways to Double Your Investment

    From risky maneuvers to slow-and-steady strategies, we look at five ways to double your money. Learn the right and wrong ways to invest for big returns.
  6. IPF - Banking

    APR and APY: Why Your Bank Hopes You Can't Tell The Difference

    Do you know the difference between Annual Percentage Rate and Annual Percentage Yield? Check out how they can affect your own account balance.
  7. Financial Advisor

    Indie BDs: Trump Should Drop the Fiduciary Rule

    A majority of independent broker-dealers want Trump to repeal the fiduciary rule, a recent survey reveals.
  8. Insights

    The DOL Fiduciary Rule Explained

    The Department of Labor (DOL) fiduciary rule expanded the “investment advice fiduciary” definition under the Employee Retirement Income Security Act of 1974 (ERISA), but was vacated by a Federal ...
  9. Tech

    Advisor Fintech Tools Aren't Waiting for Trump

    The new U.S. president might bring big change to financial regulation after he takes office. Here's how the financial technology sector is dealing.
  10. Investing

    It's Time to Re-Examine the Fees You're Paying

    It's simple: The lower your costs, the greater your share of an investment’s return. Here's why it's time to re-evaluate what you pay your advisor.
RELATED FAQS
  1. How do I calculate compound interest using Excel?

    Learn how to calculate compound interest using three different techniques in Microsoft Excel. Read Answer >>
  2. Simple versus compound interest

    Different methods in interest calculation can end up different interest payment. Learn the differences between simple and ... Read Answer >>
Trading Center