Rule of 72 Calculator

Frequently asked questions

What is the Rule of 72?

The Rule of 72 is a simple formula used by investors and financial planners to estimate how long an investment takes to double at a fixed annual rate of return. Divide 72 by the annual rate and you get an approximate number of years. For example, at 6% annual return, your money doubles in about 12 years (72 / 6 = 12). The number 72 is convenient because it is divisible by 2, 3, 4, 6, 8, 9, and 12—making mental math quick and easy.

What is the Rule of 72 formula?

Years to double ≈ 72 / Annual Rate (%). The exact formula uses the natural logarithm: Years = ln(2) / ln(1 + r), where r is the decimal rate. At 6% the exact result is 11.90 years versus the rule’s 12—an error of less than 1%.

What is the difference between Rule of 72, 69.3, and 70?

Rule of 72 is most accurate in the 6–10% range—the sweet spot for typical investment returns. Rule of 69.3 is mathematically closer to ln(2)×100 and more precise for continuous compounding, such as savings accounts that compound daily. Rule of 70 is a compromise—easier to divide mentally than 69.3 and slightly more accurate than 72 at lower rates.

How accurate is the Rule of 72?

At 6–8% the approximation error is under 0.5%. At 1% the rule overestimates doubling time by about 3% (72 years vs the exact 69.7 years). At 20%+ it underestimates by a growing margin. For rates between 4% and 12% the rule is reliable enough for quick estimates. The comparison table above shows exact errors at each rate.

What are real-world doubling times?

S&P 500 (~10% historical average): doubles every ~7.2 years. Treasury Bonds (~3% average): doubles every ~24 years. Real Estate (~7% appreciation): doubles every ~10.3 years. High-Yield Savings (~4.5% APY): doubles every ~16 years. Inflation (~3%): purchasing power halves every ~24 years—a reminder that nominal doubling does not always mean real wealth growth.

How long does it take to double $10,000?

At 5% → ~14.4 years. At 7% → ~10.3 years. At 10% → ~7.2 years. The starting amount does not matter—the doubling time depends only on the rate.

What rate do I need to double my money in 10 years?

Rule of 72: 72 / 10 = 7.2%. The exact answer using the log formula is 7.18%. Use the “Time → required rate” mode above to calculate any target.

What are the limitations of the Rule of 72?

The Rule of 72 assumes a fixed annual rate of return and compound interest only, not simple interest. It becomes less precise at very low rates (under 4%) or very high rates (over 12%). It also does not account for additional contributions, taxes, or inflation. For precise calculations, use the exact logarithmic formula shown in the comparison table above.

Can I use the Rule of 72 for debt?

Yes. The Rule of 72 works for any fixed compounding rate, including debt. At 20% credit card interest, your unpaid balance doubles in roughly 3.6 years (72 / 20) if you make no payments. This makes the rule a powerful illustration of why high-interest debt grows rapidly and should be addressed early.

What is the Rule of 115 for tripling money?

While the Rule of 72 estimates doubling time, the Rule of 115 estimates tripling time: divide 115 by the annual rate. At 8%, money triples in about 14.4 years (115 / 8). The exact formula is ln(3) / ln(1 + r). Like the Rule of 72, the approximation is most accurate in the 6 to 10% range.