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Rule of 72 Calculator

Find how long it takes to double your money at any interest rate. Compare savings, investments, debt, and inflation side by side.

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Exact doubling time also shownWorks for debt and inflationFormula verified July 2026

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The Rule of 72 is a shortcut: divide 72 by the annual rate to estimate years to double your money.

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UAE savings account at 4.5% AED fixed deposit

T = 72 / 4.5 = 16 years to double. AED 100,000 becomes AED 200,000 in 16 years. Exact calculation: 100,000 x (1.045)^16 = 200,942 — Rule of 72 gives 16 years vs the exact 15.7 years. Accuracy: approximately 0.3 years error at 4.5%.

Equity index fund at 10% CAGR (historical S&P 500 average)

T = 72 / 10 = 7.2 years to double. AED 50,000 becomes AED 100,000 in 7.2 years, AED 200,000 in 14.4 years, AED 400,000 in 21.6 years, AED 800,000 in 28.8 years. Four doublings in 29 years = 16x growth — illustrating the power of compounding over time.

Credit card debt at 36% APR — debt doubling

T = 72 / 36 = 2 years for debt to double if unpaid. AED 20,000 in credit card debt at 36% APR grows to AED 40,000 in 2 years, AED 80,000 in 4 years if only minimum payments are made. The Rule of 72 applies identically to debt — showing why high-interest debt is financially devastating.

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What is the Rule of 72?▾

The Rule of 72 is a mental math shortcut: divide 72 by the annual interest rate (as a percentage) to approximate the number of years it takes an investment to double. At 8%, money doubles in 72/8 = 9 years. The rule works because ln(2) is approximately 0.693, and 72/100 provides a close approximation for rates between approximately 6% and 10%. It was first referenced by Luca Pacioli in 1494 in Summa de arithmetica.

How accurate is the Rule of 72?▾

The Rule of 72 is most accurate for rates between 6% and 10%, where the error is typically less than 0.3 years. At lower rates (2-3%), dividing 69 or 70 by the rate gives a more accurate result. At very high rates (20%+), the rule becomes less accurate. For any rate, the exact doubling time is: T = log(2) / log(1 + r/100).

Can the Rule of 72 apply to inflation?▾

Yes — the Rule of 72 applies to any exponential process. At 3% inflation, purchasing power halves in 72/3 = 24 years. Equivalently, prices double in 24 years. A 3% inflation rate over a 40-year working career means costs increase approximately 3.3x in total.

How do I use the Rule of 72 to compare investments?▾

Compare doubling times: at 5% (savings account), money doubles in 14.4 years. At 8% (balanced fund), in 9 years. At 12% (equity index), in 6 years. Over a 30-year horizon: AED 100,000 at 5% grows to AED 432,000; at 12% it grows to AED 2,996,000 — almost 7x more from a 7 percentage point rate difference.

What is the Rule of 69 and when should I use it?▾

The Rule of 69 (from ln(2) x 100 = 69.3) is more mathematically precise for continuous compounding. For discrete annual compounding, the Rule of 72 is typically more accurate. For very low interest rates (1-3%), Rule of 69 or 70 gives a better estimate.

Does the Rule of 72 work for debt?▾

Yes — the Rule of 72 applies equally to debt growing at a compounding rate. A credit card at 24% APR: debt doubles in 72/24 = 3 years if unpaid. For any compounding debt, the Rule of 72 shows how quickly unpaid balances grow — a powerful motivator for prioritising debt repayment.

What is the Rule of 114 and Rule of 144?▾

Extending the pattern: divide 114 by the rate for tripling time, and 144 for quadrupling time. At 8%: doubles in 9 years, triples in 14.25 years, quadruples in 18 years. These use the same approximation principle: ln(3) is approximately 1.099 and ln(4) is approximately 1.386.

At what interest rate does money double in 10 years?▾

Rearranging: rate = 72 / years. To double in 10 years, you need 72/10 = 7.2% per year. The exact required rate is (2)^(1/10) - 1 = 7.177%. UAE fixed deposits currently top out at approximately 5-5.5%; global equity indices historically average 8-10% nominal CAGR.

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The Rule of 72 is an approximation. For precise calculations, use the exact doubling time formula: T = log(2) / log(1 + r). Investment returns are not guaranteed.

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