Rule of 72: what the doubling shortcut gets right and wrong

What does the rule of 72 say, and why does it work?

The rule divides 72 by an annual growth rate to estimate the years a sum takes to double. Wikipedia describes it as a method for estimating an investment's doubling time. It applies to compound interest and not to simple interest (source: Wikipedia, Rule of 72, read 2026-10-04).

Compound interest is interest paid on the principal and on interest already added. That is how Investor.gov defines it (source: Investor.gov, Compound Interest, read 2026-10-04). Doubling is the simplest milestone to count, so a single division gives a usable answer.

The exact doubling time at r percent a year is ln(2) ÷ ln(1 + r/100). The natural log of 2 is about 0.693, which is why 69.3 is the number that suits continuous compounding. Wikipedia explains that 72 stays popular because it divides evenly by 2, 3, 4, 6, 8, 9 and 12, so the mental arithmetic is clean.

Take ₹5 lakh at 9 percent a year, compounded annually. The rule gives 72 ÷ 9 = 8 years. The exact formula gives 8.04 years. After 8 years the sum is ₹5,00,000 × 1.09^8 = ₹9,96,281, a few thousand rupees short of ₹10 lakh. The shortcut is off by about half a percent.

Where is the shortcut accurate, and where does it drift?

It is closest in the middle of the range and loosens toward the ends. Wikipedia says it gives a good approximation for annual compounding at typical rates from 6 to 10 percent, and is less accurate at higher rates (source: same page, read 2026-10-04). The rates below are examples only, each computed as 72 ÷ rate against ln(2) ÷ ln(1 + rate):

• At 6 percent a year the rule says 12.0 years and the exact answer is 11.90 years.
• At 8 percent the rule says 9.0 years and the exact answer is 9.01 years.
• At 12 percent the rule says 6.0 years and the exact answer is 6.12 years.
• At 18 percent the rule says 4.0 years and the exact answer is 4.19 years.
• At 24 percent the rule says 3.0 years and the exact answer is 3.22 years, so the shortcut is about 7 percent too fast.

Source line: arithmetic by the author from the formula on Wikipedia, Rule of 72, read 2026-10-04.

The higher the rate, the more the rule flatters the result. High rates are exactly where people reach for it, so the error is worth knowing.

What does a swinging return do to the doubling time?

A swinging return lengthens the doubling time, and the rule has no way to see it. The rule needs one fixed rate every year. Real portfolios, crypto ones above all, deliver a different number each year, and the order of those numbers changes where you end up.

Step 1: the average hides the loss

Take ₹5 lakh and suppose it gains 40 percent in year one and loses 30 percent in year two, then repeats the pair. The arithmetic average of +40 and -30 is +5 percent a year. The rule of 72 says 72 ÷ 5 = 14.4 years to double.

Now follow the rupees. Year one: ₹5,00,000 × 1.40 = ₹7,00,000. Year two: ₹7,00,000 × 0.70 = ₹4,90,000. After six years of three such pairs the sum is ₹4,70,596, below the starting ₹5 lakh. It never gets near doubling on that path.

Step 2: the compound rate is the one that counts

The compound annual rate for the pair is the square root of (1.40 × 0.70). That is the square root of 0.98, or 0.99, a loss of about 1 percent a year. The shortcut was fed 5 percent and the money compounded at minus 1 percent.

Wikipedia calls this gap the volatility tax, or volatility drag. It is the difference between the arithmetic and the geometric average of returns. It is no levy in the legal sense (source: Wikipedia, Volatility tax, read 2026-10-04). It quotes the plain version: lose 50 percent and you need 100 percent to get back to even.

Step 3: what to feed the rule instead

On a volatile holding, give the rule the compound rate delivered over a stretch you can name. Never give it the average of the yearly figures. A history is a record of what happened. It is never a promise of the next stretch, and no rate in this piece is a forecast.

How deep a fall can go before a position stops doing its job is a sizing question. What a drawdown is and how a position is sized to survive one covers it.

What do costs do to the doubling time?

Costs lower the rate the rule should be given, and the doubling time grows quickly as they rise. Suppose a holding grows at 10 percent a year before costs. The rule says 72 ÷ 10 = 7.2 years to double, and the exact figure is 7.27 years.

Now take 2 percentage points of annual cost out. The growth you keep is 8 percent, and 72 ÷ 8 = 9 years, with the exact figure 9.01 years. On ₹5 lakh, doubling to ₹10 lakh takes about 1.8 years longer because of the cost alone.

Wikipedia uses the same trick the other way round. A 3 percent annual fee halves an account's value in 72 ÷ 3 = 24 years, against holding the same investment outside that fee-charging policy (source: Wikipedia, Rule of 72, read 2026-10-04). Dividing 72 by a cost tells you how long that cost takes to eat half.

So when you read a fee schedule, run the division. A cost that looks small per year is a long clock when it runs for a decade.

What does the rule leave out?

It leaves out everything that happens between the growth and your pocket. The first is tax. The rule describes the pre-tax path, and tax falls on the gain at sale, so the money that reaches you is lower than the doubled figure on the screen. The exact amount depends on the rules that apply to the asset when you sell it.

The second is inflation. The same division tells you how fast buying power halves. Wikipedia gives the example of 3.5 percent inflation and the rule of 70, which halves buying power in 70 ÷ 3.5 = 20 years. Take 6 percent as an illustrative rate and the answer is 72 ÷ 6 = 12 years. A ₹1 crore sum that stays untouched for 12 years then buys what ₹50 lakh bought at the start. What inflation does to money that sits still works through it.

The third is time itself. The rule assumes the sum stays in and no one adds or withdraws. Add ₹25,000 every month and the doubling arithmetic no longer applies to a single sum, because each deposit starts its own clock. That is why a recurring plan is judged on the total it builds and the discipline it keeps, and never on a single doubling date.

How do you use the rule without turning it into a promise?

Use it backwards: ask what a goal requires, and read the answer as a requirement.

If ₹5 lakh has to become ₹10 lakh in 6 years, the rule says 72 ÷ 6 = 12 percent a year. The exact requirement is the sixth root of 2 minus 1, which is 12.25 percent a year. That is the rate the plan needs. The market supplies whatever rate it supplies.

Read that way, the rule is a sanity check on a plan. A target that needs 24 percent a year every year is asking for something most portfolios cannot repeat, and the rule exposes it in one line. My view: the rule is best at telling you that a goal is too ambitious for its time frame, and worst at telling you when you will get there.

Where does a Qatobit index sit in this arithmetic?

Qatobit is a crypto index investing platform in India. Its four QSI Crypto Indices are baskets that Qatobit designs and rebalances monthly on a published methodology. Crypto SIP is automated recurring investment on a weekly, biweekly or monthly cadence. Both carry no promised rate, so the rule has nothing to divide by.

What the structure gives you is inputs you can read. The rebalancing rule is published and the cadence is fixed. The fee schedule sits on the index pages, so the cost line in the doubling arithmetic is a number you can look up. Crypto prices move from year to year, so the compound rate you earn will differ from any rate used in an example here.

The compounding behind the rule has two earlier pieces. One is what compounding is and why time beats the rate. The other is what the power of compounding does over a working life. For how a schedule of recurring buys works, see how a crypto SIP works. The next question after doubling is how long a plan can sit through a fall, which is the drawdown piece above.

Frequently asked questions

What is the rule of 72?

The rule of 72 estimates the years an investment takes to double by dividing 72 by the annual growth rate in percent. At 9 percent a year the answer is 72 ÷ 9 = 8 years, against an exact 8.04 years.

How accurate is the rule of 72?

It is accurate for steady annual rates of about 6 to 10 percent, where the error stays near 1 percent. At 24 percent the rule gives 3.0 years against an exact 3.22 years, so it runs fast at high rates.

Does the rule of 72 work when returns swing from year to year?

No. It needs one fixed rate. A path of +40 percent then -30 percent averages +5 percent a year but compounds at about -1 percent. ₹5 lakh ends at ₹4,70,596 after six years and does not double.

Can I use the rule of 72 to work out what fees cost?

Yes. Divide 72 by the annual cost to see how long it takes to halve the account. A 3 percent annual cost halves it in 72 ÷ 3 = 24 years. Two percentage points of cost on a 10 percent rate stretch a doubling from 7.2 to 9 years.

Is the rule of 72 a forecast of what my money will do?

No. It is arithmetic on a rate you supply. The rate is an assumption, and a rate taken from the past is a record of what happened, never a promise of what comes next.

Crypto investments are subject to market risk. Not financial advice.