Rule of 72 (and the exact doubling formula)

The Rule of 72 is a shortcut for exponential growth. When money compounds at a steady rate, the value grows like this:

Compound growth: Future Value = Present Value × (1 + r)^t

Here, r is the annual rate as a decimal (so 8% = 0.08), and t is time in years. To find the time it takes to double, set Future Value / Present Value = 2:

2 = (1 + r)^t

Solving for t gives the exact doubling-time formula:

t = ln(2) ÷ ln(1 + r)

That’s accurate, but not something you can do in your head. The Rule of 72 replaces the logarithms with a simple division:

• Years to double ≈ 72 ÷ (rate in %)
• Rate in % ≈ 72 ÷ (years to double)

Why 72? Because the constant behind the scenes is about 69.3 (from 100 × ln(2)), and 72 is a close, practical substitute that’s easy to divide by many common interest rates. The “best” constant depends on the rate range and compounding details, but 72 is the classic choice because it balances simplicity and accuracy for everyday finance.

• It’s usually quite good for rates in the ~6%–10% range.
• At very low rates (1–3%), it can under/over-estimate more noticeably.
• At high rates (15%+), it becomes rougher — but still gives quick intuition.

Examples you can copy (and sanity-check)

Below are practical examples that show why this shortcut is so popular for quick decisions and comparisons.

Rule of 72: 72 ÷ 8 = 9 years. So $10,000 might become about $20,000 in ~9 years at 8% (assuming compounding and a stable return). The exact doubling time is very close.

Rule of 72: 72 ÷ 3 = 24 years. That’s a long time — which is why higher yield or additional contributions matter for big goals.

Rule of 72: 72 ÷ 6 = 12 years. This is the “prices double” interpretation: if inflation stays at 6% for 12 years, the price level could roughly double, meaning your money buys about half as much.

Reverse Rule of 72: 72 ÷ 5 = 14.4%. That’s an aggressive target, which helps set expectations. The exact required rate may differ slightly depending on compounding frequency.

How to use this calculator (without overthinking)

People use the Rule of 72 for the same reason they use back-of-the-envelope estimates: it speeds up decisions. If you’re comparing savings accounts, investment assumptions, or inflation scenarios, you often don’t need a perfect answer — you need a fast answer that’s “close enough” to guide your next step.

• Pick a mode. Either you know the rate and want the doubling time, or you know the time and want the rate.
• Enter one value. Use annual rate in percent (like 7.5) or years (like 10).
• Choose compounding for the exact check (annual/monthly/daily/continuous).
• Read both results. The calculator returns the Rule-of-72 estimate and the exact comparison.
• Use the gap as a “confidence cue.” If the estimate and exact are close, the shortcut is plenty good.

• Investing: sanity-check a return assumption (“8% doubles in ~9 years”).
• Savings: understand why low rates feel slow (“2% doubles in ~36 years”).
• Inflation: translate inflation into “price doubling” intuition.
• Business growth: approximate how quickly revenue could double at a steady growth rate.

The key is to treat this as an estimator, not a promise. Real-world returns fluctuate; inflation changes; taxes, fees, and contributions matter. But as a mental model, the Rule of 72 is one of the cleanest tools for building “financial intuition” quickly.

Frequently Asked Questions

• Is the Rule of 72 only for investing?

  No. It applies to any situation with compounding or exponential growth: savings interest, inflation, population growth, revenue growth, and more.

• Why 72 instead of 69.3?

  69.3 (≈ 100 × ln(2)) is closer to the math, but 72 divides nicely by many common rates, making it easy mental arithmetic. The accuracy difference is usually small around everyday interest rates.

• How accurate is it?

  It’s typically quite close for moderate rates (often single digits). As rates get very small or very large, the error grows. That’s why this calculator shows the exact result too.

• Does compounding frequency matter?

  Yes, slightly. Monthly or daily compounding can change the exact doubling time a bit. The Rule of 72 ignores that detail, so it’s best seen as a quick approximation.

• Can I use it for “tripling” time?

  Rule of 72 is specifically for doubling (2×). For tripling (3×), you’d want the exact formula t = ln(3) ÷ ln(1 + r), or a separate shortcut rule.

• What if my rate changes every year?

  Then there isn’t a single clean doubling time. You can use an average return as a rough guide, but a year-by-year projection is better for accuracy.

• What if inflation is 7% — does everything really double in ~10 years?

  It’s an estimate: 72 ÷ 7 ≈ 10.3 years. Real inflation fluctuates, but the shortcut is a useful way to translate “7% inflation” into a concrete, intuitive timeline.

• Is this financial advice?

  No. This calculator is educational. For decisions involving risk, taxes, or large amounts of money, consult qualified professionals and do your own due diligence.