Rule of 72 Calculator
THE RULE OF 72
Double your money, in your head
1 lakh
AT 12% A YEAR
Exactly: 6.12 years to double. The shortcut is 1.9% low.
4.9 times
it doubles in 30 years
Rs 29.96 lakh
after 30 years (29.96×)
WHICH RULE IS CLOSEST
At 12%, the rule of 72 wins
- Exact6.12 years
- Rule of 72-1.9%6 years
- Rule of 70-4.6%5.83 years
- Rule of 69.3-5.6%5.77 years
72 is closest near 8%, 70 suits low rates like inflation, and 69.3 is right for money that compounds every day. All three slip at high rates.
INFLATION RUNS IT BACKWARDS
At 7% inflation, a rupee halves in 10.2 years
10.3 years
72 ÷ 7: prices double
Rs 13,137
what Rs 100,000 buys in 30 years, in today's prices
Growing at 12%, you stay 5% ahead
See Pakistan inflation history for real figures.
| Return | Exact years | Rule of 72 | 72 error | Rule of 70 | Rule of 69.3 |
|---|---|---|---|---|---|
| 2% | 35 | 36 | +2.8% | 35 | 34.65 |
| 3% | 23.45 | 24 | +2.3% | 23.33 | 23.1 |
| 4% | 17.67 | 18 | +1.9% | 17.5 | 17.32 |
| 5% | 14.21 | 14.4 | +1.4% | 14 | 13.86 |
| 6% | 11.9 | 12 | +0.9% | 11.67 | 11.55 |
| 7% | 10.24 | 10.29 | +0.4% | 10 | 9.9 |
| 8% | 9.01 | 9 | -0.1% | 8.75 | 8.66 |
| 9% | 8.04 | 8 | -0.5% | 7.78 | 7.7 |
| 10% | 7.27 | 7.2 | -1% | 7 | 6.93 |
| 11% | 6.64 | 6.55 | -1.5% | 6.36 | 6.3 |
How the rule of 72 works
Money growing at a steady yearly rate doubles after a fixed time, no matter how big it is. The exact time comes from logarithms, which is awkward to do in your head. The rule of 72 replaces them with a division: divide 72 by the return and you have the doubling time in years. The calculator shows both so you can see how close the shortcut gets.
- r
- annual return in percent (12% is 12)
- n
- years to double
Running it backwards gives the return needed: r ≈ 72 ÷ n, with the exact value 2^(1/n) − 1. The same logic extends to other multiples: the rule of 114 for tripling and 144 for quadrupling.
Rule of 72 vs the exact answer
The shortcut is most accurate around 8% and drifts at the extremes. Here is how long money takes to double, exactly and by each rule.
| Return | Exact years | Rule of 72 | Rule of 70 | Rule of 69.3 |
|---|---|---|---|---|
| 2% | 35 | 36 | 35 | 34.65 |
| 4% | 17.67 | 18 | 17.5 | 17.32 |
| 6% | 11.9 | 12 | 11.67 | 11.55 |
| 8% | 9.01 | 9 | 8.75 | 8.66 |
| 10% | 7.27 | 7.2 | 7 | 6.93 |
| 12% | 6.12 | 6 | 5.83 | 5.77 |
| 15% | 4.96 | 4.8 | 4.67 | 4.62 |
| 20% | 3.8 | 3.6 | 3.5 | 3.46 |
| 30% | 2.64 | 2.4 | 2.33 | 2.31 |
At 8% the rule of 72 is almost perfect (9 against 9.01). At 2% it overstates the time (36 years against 35), and at 30% it understates it (2.4 against 2.64). For low rates the rule of 70 does better, and for high rates use the exact figure, which the calculator always gives.
The return you need to double in a set time
Planning backwards is just as useful: if you want to double your money by a certain date, what return do you need?
| To double in | Exact return needed | 72 ÷ years |
|---|---|---|
| 3 years | 25.99% | 24% |
| 5 years | 14.87% | 14.4% |
| 7 years | 10.41% | 10.29% |
| 10 years | 7.18% | 7.2% |
| 15 years | 4.73% | 4.8% |
Doubling in 5 years needs about 14.9% a year, which a bank deposit will rarely offer, so a goal like that usually needs equity risk, more time or regular additions. Test your own plan in the compound interest calculator or the SIP calculator.
How fast inflation halves your rupee
The rule works against you too. If prices rise at a steady rate, money loses half its buying power in the same time it takes an investment to double at that rate. Here is what Rs 100,000 buys after ten years at different inflation rates.
| Inflation | Rupee halves in | Rs 100,000 buys, after 10 years, what this buys today |
|---|---|---|
| 5% | 14.2 years | Rs 61,391 |
| 7% | 10.2 years | Rs 50,835 |
| 12% | 6.1 years | Rs 32,197 |
| 20% | 3.8 years | Rs 16,151 |
| 30% | 2.6 years | Rs 7,254 |
Pakistan has seen both ends: inflation in single digits for stretches, and a peak near 38% in May 2023. If a rate like that were sustained for a year, a rupee would lose half its value in about 2.2 years at that pace. That is why a return only counts if it beats inflation. See the real history in the inflation calculator, and read the CAGR calculator to turn a past result into a yearly rate.
Where the rule of 72 falls short
- It assumes one steady rate. Real returns, especially on shares, rise and fall, so actual doubling time varies.
- It ignores tax, fees and inflation. Use an after-tax, after-inflation rate to learn when your purchasing power doubles.
- It works on money left to compound. Regular withdrawals (try the SWP calculator) or deposits change the answer.
- It is a mental shortcut. When the decision matters, use the exact figure the calculator shows.
Sources and assumptions
- Exact doubling time: ln 2 ÷ ln(1 + r); exact rate to double in n years: 2^(1/n) − 1
- Shortcuts: 72 ÷ r, 70 ÷ r and 69.3 ÷ r (years), 72 ÷ n (rate); the rule of 114 and 144 for tripling and quadrupling
- Pakistan Bureau of Statistics: Consumer Price Index, for real inflation history
Results are estimates for information and planning only, not tax, legal or investment advice. Check your own case with a tax adviser, your broker or the official source before acting.
FAQ
Rule of 72 Calculator: common questions
What is the rule of 72?+
The rule of 72 is a mental shortcut: divide 72 by your yearly return in percent to estimate how many years it takes money to double. At 12% a year, 72 ÷ 12 is 6 years. The exact answer is 6.12 years, so the shortcut is within about 1.9%.
Why 72 and not 70 or 69.3?+
The exact doubling time is ln 2 ÷ ln(1 + r), and for small rates it is close to 69.3 ÷ r. Rates around 8% give a number near 72, and 72 divides neatly by 2, 3, 4, 6, 8, 9 and 12, which makes mental maths easy. The rule of 70 is slightly better for low rates such as 2% to 5%, and 69.3 suits continuous compounding. All three are within a few percent for typical returns.
How accurate is the rule of 72?+
It is very accurate between roughly 6% and 10%: at 8% the rule says 9 years against an exact 9.01. At 2% it says 36 against 35, and at 30% it says 2.4 against 2.64. The calculator shows the exact figure beside each shortcut, and a full table from 2% to 30%.
How do I find the return needed to double my money in a set time?+
Turn it around: rate ≈ 72 ÷ years. To double in 10 years you need about 7.2% a year by the rule, and exactly 7.18%. Choose Rate needed in the calculator to get the exact figure for any number of years.
Can I use it for inflation?+
Yes, in the opposite direction. Prices double, and money loses half its buying power, in about 72 ÷ inflation years. At 7% inflation that is roughly 10 years. If inflation ran at 38% for a year, as it did at its May 2023 peak, a rupee would lose half its purchasing power in about 2.2 years at that pace. The calculator has an inflation table, and the inflation calculator shows real Pakistani CPI history.
Does the rule of 72 work for PSX stocks and mutual funds?+
It works as a shortcut for an average return, such as a fund's long-run CAGR. Real stock returns are uneven, so actual doubling time will differ from the rule: markets can double money in two years or take ten. Treat the answer as a planning guide, not a promise.
Is there a rule for tripling or quadrupling money?+
Yes. The rule of 114 estimates tripling time (114 ÷ rate) and the rule of 144 estimates quadrupling (144 ÷ rate). At 10% the rules give 11.4 and 14.4 years against exact figures of 11.5 and 14.5.
Keep going
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