Rule of 72 Calculator
See how long your money takes to double, the quick way (72 ÷ rate) and the exact way, side by side.
Rule of 72 vs exact, 1% to 20%
| Rate | Rule of 72 | Exact | Off by |
|---|
How your doubling time is worked out
Quick rule: years ≈ 72 ÷ rate. Exact: years = ln 2 ÷ ln(1 + rate).
- 1
The quick rule
72 ÷ 8≈ 9 years
- 2
The exact sum
ln 2 ÷ ln 1.080.6931 ÷ 0.0770= 9.01 years
- 3
How close it is
9 vs 9.01 yrsOff by 0.07%
- 4
It keeps doubling
2× in 9 yrs4× in 18 yrs8× in 27 yrsSame time each
Read more: the formula, a worked example, why 72 and the 1–20% table
The rule of 72 is a shortcut for compound growth. Divide 72 by the yearly rate and you get roughly how many years it takes for money to double. Turn it round, divide 72 by the years, and you get the rate you need.
The formula
quick rule: years to double ≈ 72 ÷ yearly rate (in %)
rate needed ≈ 72 ÷ years
exact: years = ln 2 ÷ ln(1 + rate ÷ 100)
compounded n times a year: years = ln 2 ÷ (n × ln(1 + rate ÷ 100 ÷ n))
continuously: years = ln 2 ÷ (rate ÷ 100) = 69.3 ÷ rate
triple: use 114 and ln 3 · quadruple: use 144 and ln 4
"ln" is the natural log, the button marked ln on a calculator. ln 2 = 0.6931, ln 3 = 1.0986 and ln 4 = 1.3863.
Worked example
At 8% a year, compounded yearly. The quick rule: 72 ÷ 8 = 9 years. The exact answer: ln 2 ÷ ln 1.08 = 0.693147 ÷ 0.076961 = 9.0065 years, about 9 years and 2 days. Check: 1.089 = 1.9990, so after exactly 9 years your money has grown 1.999 times, just short of double. The rule is off by 0.0065 years, or 0.07%. So 10,000 becomes 20,000 after 9.01 years, 40,000 after 18.01 years and 80,000 after 27.02 years.
To double in 10 years you need 72 ÷ 10 = 7.2% a year by the rule, or exactly 21/10 − 1 = 7.177%.
Why 72?
The exact number for continuous compounding is 100 × ln 2 = 69.31, usually rounded to 69.3. Yearly compounding needs a slightly bigger number, and at typical rates 72 is very close: with yearly compounding the rule of 72 is exact at about 7.85%. 72 also has lots of divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72), so 72 ÷ 6, 72 ÷ 8 or 72 ÷ 9 are easy in your head. 70 divides by 1, 2, 5, 7, 10, 14 and 35, which suits low rates. For high rates, the adjusted rule adds 1 for every 3 points above 8%: at 20%, 72 + 4 = 76, and 76 ÷ 20 = 3.8 years against an exact 3.80.
Rule of 72 and 70 against the exact answer
| Rate | 72 ÷ rate | 70 ÷ rate | Exact, yearly |
|---|---|---|---|
| 1% | 72.00 | 70.00 | 69.66 |
| 2% | 36.00 | 35.00 | 35.00 |
| 4% | 18.00 | 17.50 | 17.67 |
| 6% | 12.00 | 11.67 | 11.90 |
| 8% | 9.00 | 8.75 | 9.01 |
| 10% | 7.20 | 7.00 | 7.27 |
| 12% | 6.00 | 5.83 | 6.12 |
| 15% | 4.80 | 4.67 | 4.96 |
| 20% | 3.60 | 3.50 | 3.80 |
Inflation: when money loses half its value
The same rule works backwards for prices. At 6% inflation prices double in about 72 ÷ 6 = 12 years (exactly ln 2 ÷ ln 1.06 = 11.90), so 100,000 kept in cash buys what 50,000 buys today. After about 24 years it buys a quarter.
The quick rules assume a steady rate and no fees or tax. Real returns go up and down, so treat the answer as a guide. Taxes and fees lower your rate; use the rate after them for a truer answer.
Common questions
What is the rule of 72?
It is a quick way to see how long money takes to double: divide 72 by the yearly rate. At 8% a year, 72 ÷ 8 = 9 years. The exact answer is ln 2 ÷ ln 1.08 = 9.0065 years, so the rule is off by only a couple of days.
How accurate is the rule of 72?
With yearly compounding it is exact at about 7.85% and within 3% of the right answer from about 2% to 14%. At 1% it says 72 years when the truth is 69.66; at 20% it says 3.6 years when the truth is 3.80. For high rates an adjusted rule, 72 + (rate − 8) ÷ 3, does better.
Should I use the rule of 72, 70 or 69.3?
Use 72 for yearly compounding at normal rates (about 5% to 12%). Use 70 or 69.3 for low rates or for interest compounded daily or continuously: with continuous compounding the doubling time is exactly 69.3 ÷ rate, because ln 2 = 0.693.
What are the rule of 114 and the rule of 144?
They do the same job for tripling and quadrupling. Divide 114 by the rate to see how long money takes to triple, and 144 to see how long it takes to quadruple. At 8%, money triples in about 14.25 years (exactly 14.27) and quadruples in about 18 years.
How do I use the rule of 72 for inflation?
Divide 72 by the inflation rate to see how long it takes for prices to double, which is the same as your money buying half as much. At 6% inflation that is about 12 years (exactly 11.9). Money left in cash loses half its buying power in that time.
Why 72 and not 69.3?
The exact number for continuous compounding is 100 × ln 2 = 69.31, usually rounded to 69.3, but most savings compound yearly or monthly, which pushes the right number up to about 72 at typical rates. 72 also divides neatly by 1, 2, 3, 4, 6, 8, 9 and 12, so you can do the sum in your head.
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