How accurate is the Rule of 72?

The Rule of 72 is most accurate for interest rates between 6% and 10%. At 8%, the estimate differs from the exact answer by less than 0.1%. At rates below 4% or above 15%, the error grows larger. For precise calculations, use the exact compound interest formula: t = ln(2) / ln(1 + r).

How do I use the Rule of 72 to find the required interest rate?

Divide 72 by the number of years you want to double your money in to get the required annual interest rate. For example, to double your investment in 9 years, you need an interest rate of approximately 72 divided by 9, which equals 8% per year.

What is the exact formula to double an investment?

The exact time to double an investment is t = ln(2) / ln(1 + r), where r is the interest rate as a decimal and t is the number of periods. At 6% annual interest (r = 0.06), t = ln(2) / ln(1.06) = 0.6931 / 0.05827 = approximately 11.9 years.

Rule of 72 Calculator | How Long to Double Your Money

Rule of 72 Calculator

Q: What is the Rule of 72?

The Rule of 72 is a simple formula for estimating how long it takes to double an investment at a fixed annual interest rate. Divide 72 by the annual interest rate percentage to get the approximate number of years. For example, at 6% interest, 72 divided by 6 equals 12 years to double your money.

Q: Does the Rule of 72 work for monthly interest rates?

Yes. If you enter a monthly interest rate, the answer comes out in months. For example, at 0.5% per month, 72 divided by 0.5 equals 144 months, which is 12 years. The period of the result always matches the period of the interest rate you use.

Find how long it takes to double your money, or what interest rate you need. Fast and accurate.

Annual Interest Rate

Rule of 72 Estimate

Exact Answer

Rule of 72 Reference Table

Rule of 72 reference values show how investment doubling time changes with different interest rates.

Annual Rate	Rule of 72 (years)	Exact Years	Difference
1%	72.0	69.66	2.34
2%	36.0	35.00	1.00
3%	24.0	23.45	0.55
4%	18.0	17.67	0.33
5%	14.4	14.21	0.19
6%	12.0	11.90	0.10
8%	9.0	9.01	0.01
10%	7.2	7.27	0.07
12%	6.0	6.12	0.12
15%	4.8	4.96	0.16
20%	3.6	3.80	0.20
25%	2.88	3.11	0.23
36%	2.0	2.25	0.25

What Is the Rule of 72?

The Rule of 72 is a quick mental math shortcut for estimating how long compound interest takes to double an investment. The rule states that 72 divided by the annual interest rate gives the approximate number of years to double your money.

Years to double = 72 ÷ Annual Interest Rate (%)

It also works in reverse to find the required rate: if you know how many years you want to double your money in, divide 72 by that number of years to get the required annual rate.

Required Rate (%) = 72 ÷ Years to Double

Worked Example: Doubling at 6% Per Year

Rule of 72 estimate: 72 ÷ 6 = 12 years
Exact answer: ln(2) ÷ ln(1.06) = 11.90 years
The estimate is off by only 0.10 years, less than 5 weeks.

Worked Example: Rate Needed to Double in 10 Years

Rule of 72 estimate: 72 ÷ 10 = 7.2% per year
Exact answer: 2^(1/10) – 1 = 7.18% per year
The estimate is off by only 0.02 percentage points.

The Math Behind the Rule of 72

The math behind the Rule of 72 comes from the compound interest formula and natural logarithms.

The exact doubling time formula is: t = ln(2) ÷ ln(1 + r), where r is the interest rate as a decimal and ln is the natural logarithm.

Since ln(2) equals approximately 0.6931, and for interest rates near 8% the term r ÷ ln(1+r) is approximately 1.0395, we get: t × r ≈ 0.6931 × 1.0395 ≈ 0.72. Multiplying both sides by 100 to use percentage rates gives: R × t = 72.

The rule is most accurate between 6% and 10% because that is where the approximation was calibrated. It becomes less accurate at very low rates (below 3%) and high rates (above 20%).

Rule of 72 for Monthly Rates

The Rule of 72 works for any period, not just years. If your interest rate is monthly, the answer comes out in months. At 0.5% per month: 72 ÷ 0.5 = 144 months, which equals 12 years. This is useful for savings accounts or loans with monthly compounding.

Practical Uses of the Rule of 72

Practical uses of the Rule of 72 go far beyond investing. The rule applies to any exponential growth or decay.

Inflation: At 4% annual inflation, prices double in roughly 72 ÷ 4 = 18 years. Your purchasing power halves in the same time.
Debt: An unpaid credit card at 18% APR doubles the balance owed in 72 ÷ 18 = 4 years.
GDP growth: A country growing at 3% per year doubles its economy in about 24 years.
Population: A population growing at 2% per year doubles in about 36 years.
Comparing investments: A quick way to compare options without a calculator. An 8% fund doubles in 9 years while a 4% fund takes 18 years.

Frequently Asked Questions

The Rule of 72 is a quick estimation formula: divide 72 by the annual interest rate to get the approximate number of years needed to double an investment. For example, at 6% interest, 72 divided by 6 equals 12 years. It works in reverse too: divide 72 by the number of years to get the required annual rate.

The Rule of 72 is most accurate for interest rates between 6% and 10%, where the error is less than 0.1 years. At 1% the estimate is about 2.3 years off and at 25% the error grows to about 0.2 years. For rates in this middle range, the rule is a very reliable quick estimate without needing a calculator.

Divide 72 by the number of years you want to double your money in. For example, to double your investment in 9 years, you need 72 divided by 9, which equals 8% annual interest. To double in 6 years, you need 72 divided by 6, which equals 12% per year.

Yes. If you enter a monthly interest rate, the result comes out in months. At 0.5% per month: 72 divided by 0.5 equals 144 months, which is 12 years. Always match the period of the rate to the period you want the answer in.

The exact time to double is t = ln(2) divided by ln(1 + r), where r is the interest rate expressed as a decimal (not a percentage). For 6% interest (r = 0.06), t = 0.6931 divided by 0.05827 = 11.90 years. This calculator shows both the Rule of 72 estimate and this exact result.

Yes. At 4% annual inflation, your purchasing power halves in approximately 72 divided by 4 = 18 years. The rule applies to any exponential growth or decay, including inflation, population growth, debt accumulation, or GDP growth.