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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.

Doubling Time Worksheet
%
$
Estimated time 11.077 yrs
Rule-of-72 estimate. 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

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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 estimates how many years it takes money to double: divide 72 by the annual rate of return. At 8% growth, money doubles in about 72 / 8 = 9 years. At 6% it takes about 12 years, and at 12% about 6 years. It works for anything that compounds, including inflation and debt.

How accurate is the Rule of 72?

The Rule of 72 is most accurate for rates between 6% and 10%, and at 8% it is almost exact. The precise doubling time is ln(2) / ln(1 + r): at 8% that is 9.006 years against the estimate of 9. Below 6% or above 10% the estimate drifts, and the Rule of 69.3 or Rule of 70 can be closer.

What return do I need to double my money in 10 years?

About 7.2% a year, found by dividing 72 by 10. The exact rate is 7.177%, from (2^(1/10) - 1) × 100. The same shortcut works for any target: doubling in 6 years needs about 12% a year, and doubling in 12 years needs about 6%.

How does the Rule of 72 apply to debt and inflation?

Divide 72 by the rate to see how fast a debt doubles or purchasing power halves. Unpaid credit card debt at 18% interest doubles in about 72 / 18 = 4 years. At 3% inflation prices double in about 24 years, and at 4% inflation the purchasing power of a dollar halves in about 18 years.