How long to double your money at 4%?

    Divide 72 by your annual return and you know when your money doubles. At 7% that is 10.3 years. This calculator compares the quick estimate to the exact compound formula and shows year-by-year growth.

    At 4% annual return, the Rule of 72 gives you a quick estimate of how long it takes to double your investment. Simply divide 72 by 4 and you get the approximate number of years. This shortcut works for savings accounts, index funds, bonds, real estate appreciation, and even inflation erosion. Enter 4 in the interest rate field below to see exact doubling time, tripling time, and a full growth projection table.

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    A mental shortcut invented before spreadsheets that still beats most compound interest tables

    Divide 72 by your annual return rate. The result is the number of years until your money doubles. At 7%, that is 10.3 years. At 12%, just 6 years. The Rule of 72 has been in use since at least 1494 (Luca Pacioli mentioned it in Summa de Arithmetica) and remains the fastest way to estimate compound growth without a calculator. This tool compares the quick estimate to the exact formula and shows where the approximation breaks down.

    How to use this calculator - step by step

    1. Calculator mode - choose whether you know the return rate (and want the time) or you have a target time (and need the rate). Two completely different questions, one tool.
    2. Annual return rate - enter the expected yearly return. Use nominal rates (before inflation). S&P 500 historical: ~10%. Bonds: 4-6%. Savings accounts: 4-5%.
    3. Target years - alternatively, enter how many years you want to double in. The calculator tells you what return rate you need.
    4. Starting amount (optional) - add a dollar amount to see a year-by-year growth table with the exact doubling point highlighted.
    5. Read the result - you get both the Rule of 72 estimate and the exact compound calculation side by side, plus a precision assessment.

    Rule of 72 accuracy by rate

    The approximation is most accurate between 4% and 12%. Outside that range, the error grows:

    Annual rate Rule of 72 Exact (years) Error
    2% 36.0 35.0 +1.0 yr
    5% 14.4 14.2 +0.2 yr
    7% 10.3 10.2 +0.1 yr
    10% 7.2 7.3 -0.1 yr
    15% 4.8 5.0 -0.2 yr
    25% 2.9 3.1 -0.2 yr
    50% 1.4 1.7 -0.3 yr

    Practical examples

    Example 1: S&P 500 index fund at 10%
    Rule of 72: 72/10 = 7.2 years to double. Exact: 7.27 years. $10,000 becomes $20,000.
    Example 2: High-yield savings at 4.5%
    Rule of 72: 72/4.5 = 16.0 years to double. Exact: 15.7 years. Safe but slow.
    Example 3: Want to double in 5 years - what rate?
    Rule of 72: 72/5 = 14.4% needed. Exact: 14.87%. Aggressive growth territory.
    Example 4: Bond portfolio at 6%
    Rule of 72: 72/6 = 12.0 years. Exact: 11.9 years. $50,000 becomes $100,000.
    Example 5: Crypto speculation at 30%
    Rule of 72: 72/30 = 2.4 years. Exact: 2.64 years. High return but Rule of 72 less accurate here.
    Example 6: $100,000 at 7% for retirement
    Doubles to $200,000 in 10.3 years, then to $400,000 in 20.5 years, and $800,000 in 30.7 years. Three doublings.

    FAQ - Frequently asked questions

    Why does the Rule of 72 work?
    The natural logarithm of 2 is 0.6931. For small interest rates, ln(1+r) is approximately r. So the doubling time = ln(2)/ln(1+r) is approximately 0.6931/r. Multiply numerator and denominator by 100: that gives 69.3/rate. The number 72 is used instead of 69.3 because it has more divisors (2, 3, 4, 6, 8, 9, 12) making mental division easier, and it also partially compensates for the approximation error at typical investment rates (6-10%).
    When should I use Rule of 69 or Rule of 70 instead?
    For continuous compounding, use 69.3 (the exact value of 100 x ln(2)). For rates above 20%, Rule of 69 gives a better estimate. Rule of 70 splits the difference and works well for rates between 2% and 20%. Rule of 72 is best for the typical 6-12% range because the rounding error of 72 vs 69.3 cancels out part of the discrete compounding error.
    Does inflation affect the doubling time?
    Yes. The Rule of 72 gives nominal doubling time. If your investment returns 7% but inflation is 3%, your real (purchasing power) return is only ~4%. Real doubling time: 72/4 = 18 years, not 10. Always subtract inflation to see what your money can actually buy when it doubles.
    Can I use this for debt too?
    Absolutely. If your credit card charges 18% interest: 72/18 = 4 years for your debt to double if you make no payments. A payday loan at 400% APR? The debt doubles in just 66 days. The Rule of 72 shows why high-interest debt is an emergency.
    How many times does money double over a career?
    At 7% (stock market average), money doubles every ~10 years. Over a 40-year career: 4 doublings. $10,000 at age 25 becomes roughly $160,000 at age 65 without adding a single dollar. Start at 35 instead (30 years = 3 doublings): only $80,000. One decade of delay costs half the final amount.
    What is the exact formula for doubling time?
    Exact doubling time = ln(2) / ln(1 + r), where r is the decimal rate (7% = 0.07). For the reverse question (what rate to double in T years): rate = 2^(1/T) - 1. Both formulas use the compound interest equation A = P(1+r)^t, solved for t or r with A = 2P.

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    See also

    Rule of 72 at 3% - How Long to Double Your Money?Rule of 72 at 5% - How Long to Double Your Money?Rule of 72 at 6% - How Long to Double Your Money?Rule of 72 at 7% - How Long to Double Your Money?Rule of 72 at 8% - How Long to Double Your Money?Rule of 72 at 9% - How Long to Double Your Money?Rule of 72 at 10% - How Long to Double Your Money?Rule of 72 at 12% - How Long to Double Your Money?Rule of 72 at 15% - How Long to Double Your Money?

    Calculator verified by the LiczGrupa.pl team

    Content, formulas and results have been reviewed for accuracy and relevance by our team of specialists.

    Krystian Szyszka

    Reviewed by: Krystian Szyszka

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