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Rule of 72 Calculator

Calculate the time or rate needed to double an investment using the Rule of 72. Shows both estimated and exact results with growth table.

Calculate the time needed to double an investment with a specified rate of return.

%
$
Estimated Time
11.077 yrs

The result above is an estimate using the rule of 72 formula. The actual time is 11.007 yrs

Rule of 72 Estimate
11.077 yrs
Actual (Exact)
11.007 yrs

Growth Over Time

YearRule of 72 AmountExact AmountDifference
0$5,000.00$5,000.00$0.00
1$5,322.88$5,325.00$2.12
2$5,666.60$5,671.12$4.52
3$6,032.52$6,039.75$7.23
4$6,422.07$6,432.33$10.26
5$6,836.78$6,850.43$13.65
6$7,278.27$7,295.71$17.44
7$7,748.26$7,769.93$21.67
8$8,248.61$8,274.98$26.37
9$8,781.26$8,812.85$31.59
10$9,348.31$9,385.69$37.38
11$9,951.98$9,995.76$43.78
12$10,594.63$10,645.48$50.85
Formula: Time ≈ 72 / 6.5 = 11.077 yrs
Quick Reference: Doubling Times
RateRule of 72Actual
1%72.0 yrs69.7 yrs
2%36.0 yrs35.0 yrs
3%24.0 yrs23.4 yrs
4%18.0 yrs17.7 yrs
5%14.4 yrs14.2 yrs
6%12.0 yrs11.9 yrs
7%10.3 yrs10.2 yrs
8%9.0 yrs9.0 yrs
9%8.0 yrs8.0 yrs
10%7.2 yrs7.3 yrs
12%6.0 yrs6.1 yrs
15%4.8 yrs5.0 yrs
18%4.0 yrs4.2 yrs
20%3.6 yrs3.8 yrs
24%3.0 yrs3.2 yrs

The Rule of 72

The Rule of 72 provides a quick way to estimate how long an investment takes to double:

Doubling Time ≈ 72 / Interest Rate

Or, to find the rate needed to double in a specific time:

Required Rate ≈ 72 / Years

Rule of 72 vs. Exact Calculation

RateRule of 72ExactError
2%36.0 yrs35.0 yrs+2.9%
4%18.0 yrs17.7 yrs+1.8%
6%12.0 yrs11.9 yrs+0.9%
8%9.0 yrs9.0 yrs+0.0%
10%7.2 yrs7.3 yrs-0.7%
12%6.0 yrs6.1 yrs-1.5%

Variations

  • Rule of 69.3: More accurate mathematically (69.3 = ln(2) × 100), best for continuous compounding
  • Rule of 70: Easier mental math than 69.3, good for rates below 5%
  • Rule of 72: Best for rates between 6-10%, easiest to divide mentally

Practical Applications

  • Investing: At 7% average stock market return, money doubles in about 10 years
  • Inflation: At 3% inflation, purchasing power halves in 24 years
  • Debt: Credit card debt at 18% doubles in just 4 years if unpaid
  • Savings: A savings account at 4.5% takes about 16 years to double

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Frequently Asked Questions

What is the Rule of 72?

The Rule of 72 is a shortcut to estimate how long it takes an investment to double at a given annual rate of return. Divide 72 by the interest rate to get the approximate doubling time in years. For example, at 8% growth, money doubles in about 72 / 8 = 9 years.

How accurate is the Rule of 72?

The Rule of 72 is most accurate for interest rates between 6% and 10%. At 8%, it gives exactly the right answer. Below 6% or above 10%, the estimate drifts slightly. For very high or low rates, the Rule of 69.3 or Rule of 70 may be more accurate.

What is the exact formula?

The exact doubling time is t = ln(2) / ln(1 + r), where r is the decimal interest rate. For example, at 8%: t = ln(2) / ln(1.08) = 0.6931 / 0.07696 = 9.006 years. The Rule of 72 gives 72 / 8 = 9 years — very close.

Can the Rule of 72 be used for things other than investments?

Yes. It works for anything that grows at a compound rate: inflation (how long until prices double), population growth, GDP growth, or even debt. At 3% inflation, prices double in about 72 / 3 = 24 years.

Why 72 and not another number?

72 is used because it has many divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), making mental math easy. The mathematically precise number is ln(2) × 100 ≈ 69.3, but 72 is more practical for quick calculations.

How do I find the rate needed to double my money?

Divide 72 by the number of years. To double in 10 years, you need about 72 / 10 = 7.2% annual return. The exact rate is (2^(1/10) - 1) × 100 = 7.177%.