What is the Rule of 72?

The Rule of 72 is a quick mental math shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 8% annual return, money doubles in 72 ÷ 8 = 9 years. It works best for rates between 6–10%.

How accurate is the Rule of 72?

The Rule of 72 is an approximation. The exact doubling time is ln(2) ÷ ln(1 + r) — at 8%, that's 9.006 years vs 72/8 = 9 years. The approximation is most accurate between 6–10% and less accurate at extreme rates (1% or 50%).

What is the Rule of 114 and Rule of 144?

Rule of 114: divide 114 by the annual rate to estimate years to triple your money. Rule of 144: divide 144 by the annual rate to estimate years to quadruple your money. At 10% return: double in 7.2 years, triple in 11.4 years, quadruple in 14.4 years.

Rule of 72 Calculator 2025 — How Long to Double Your Money

The Rule of 72 is a classic mental math shortcut for estimating investment doubling time. Simply divide 72 by the annual return rate to find the years to double your money. This calculator works bidirectionally: enter a rate to get years, or enter a target number of years to find the required rate. It also shows the Rules of 114 (triple) and 144 (quadruple), plus the mathematically exact values using the logarithmic formula for comparison.

✖️ Rule of 72 Input

Quick Reference

Rate	Double	Triple
4%	18.0 yr	28.5 yr
6%	12.0 yr	19.0 yr
8%	9.0 yr	14.25 yr
10%	7.2 yr	11.4 yr
12%	6.0 yr	9.5 yr

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Enter a rate or time period to calculate doubling, tripling, and quadrupling times.

The Math Behind Rule of 72

The exact doubling time uses logarithms:

Years = ln(2) / ln(1 + r) = 0.6931 / ln(1 + r)

The Rule of 72 approximates this using a simpler division: Years ≈ 72 / rate%. The number 72 works because it's close to 100 × ln(2) = 69.3 and is divisible by many common rates (2, 3, 4, 6, 8, 9, 12). For more accuracy at high rates, use 70 instead of 72.

Frequently Asked Questions

The mathematically precise constant is 69.3 (100 × ln 2). Rule of 70 is also used. Rule of 72 is popular because 72 is highly composite — divisible by 2, 3, 4, 6, 8, 9, 12, 24 — making mental math easier. At 8%: 72÷8=9 (exact: 9.006). At 6%: 72÷6=12 (exact: 11.9). Rule of 72 is slightly more accurate than 70 for the 6–10% range.

The Rule of 72 works for inflation too. At 3% inflation, prices double in 72÷3 = 24 years. At 7% inflation (as in 2022), prices double in about 10 years. This is why sustained inflation above 3% significantly erodes savings and why real returns (nominal − inflation) matter more than nominal returns.

Historical average annual returns: US stocks (S&P 500): ~10% nominal, ~7% real. International stocks: ~7% nominal. Bonds (10-yr Treasury): ~4–5% nominal. Real estate (REITs): ~9–10%. High-yield savings accounts: ~4–5% (2025). Inflation (~2.5–3%) erodes these returns in real terms.

Rule of 72 Calculator

The Math Behind Rule of 72

Frequently Asked Questions

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