Rule of 72 Calculator

The mental model that replaces a calculator

Divide 72 by the interest rate; the answer is roughly how many years until the money doubles. At 7%, money doubles in about 10.3 years. At 8%, 9 years. At 4%, 18 years. At 12%, 6 years. The rule is approximate but accurate within a fraction of a year across typical investment rates, and it's fast enough to run in your head during a conversation. That speed is why it survives as a useful tool a century after better calculators became available.

Why it works

The precise doubling time is ln(2) / ln(1 + r), where r is the decimal rate. For small rates, this approximates to 0.693 / r. For compounded integer rates (like percentages), 72 works better than the theoretical 69.3 because 72 has more integer divisors — it divides cleanly by 2, 3, 4, 6, 8, 9, 12. This makes mental arithmetic easy across the common rate range. At higher rates (above 12%), the rule slightly underestimates; at lower rates it slightly overestimates. For rates between 6% and 10% — where most real investment decisions live — the error is under 3% of the true doubling time. Outside that band the approximation is still useful as a rough check, just less precise.

Applied to common financial questions

The rule works directly on any compound growth or decay. Some real applications:

How long until my investment doubles? At 7% real return: 72/7 = 10.3 years.

How long until inflation halves my money's value? At 3% inflation: 72/3 = 24 years. At 5% inflation: 14 years.

How long until my credit card balance doubles if I pay only the interest? At 22% APR: 72/22 = 3.3 years.

What rate do I need for my money to double in 10 years? 72/10 = 7.2% annual return.

What rate would double my debt in 5 years? 72/5 = 14.4% — the rate at which credit card or subprime debt becomes hard to pay off.

Where the rule breaks down

The Rule of 72 assumes annual compounding and positive compound growth. It does not work for simple-interest products (use 100/rate × years instead), for highly variable returns where the average hides large swings, or for very high rates above 20% (where the error grows). For these cases, the explicit calculation is more reliable than the rule.

The loss-recovery problem (a separate issue)

Loss recovery is often confused with the Rule of 72, but it is a different concept worth understanding on its own. Losing 50% requires gaining 100% to recover — not because the Rule of 72 breaks, but because percentages are asymmetric. A portfolio that drops from 10,000 to 5,000 has lost half its value. Bringing it back to 10,000 requires doubling the remaining 5,000, which is a 100% gain. This asymmetry is why drawdowns hurt more than equivalent-percentage rallies help. Use explicit compound-growth math for recovery scenarios — the Rule of 72 applies only to steady positive growth.

The Rule of 114 (tripling) and Rule of 144 (quadrupling)

Less famous siblings that work the same way. 114 divided by rate = years to triple. 144 divided by rate = years to quadruple. At 7%, money triples in 16.3 years and quadruples in 20.6 years. Combined with doubling time, these three rules let you mentally chart a growth trajectory across any sensible rate. The pattern: after one doubling, another doubling, then roughly another half-doubling gets you to 4×. Visualising the curve this way beats trying to remember specific multipliers for specific years.

The 70 variant and when it's better

Some financial resources use 70 instead of 72. Mathematically, 70 is closer to the true constant (69.3). The argument for 72 is easier mental math (72 divides more cleanly). The argument for 70 is marginally better accuracy at very low rates. At 2% inflation, 70/2 = 35 years vs 72/2 = 36 years vs true 35 years. The difference is one year across a 35-year horizon — real but small. Either works for practical purposes. The cultural default in finance is 72; in economics (where lower rates matter more), 70 is sometimes preferred.

Using the rule to spot bad math

The rule is most useful as a reality check on claims. A pitch to double an investment in 4 years implies a 72/4 = 18% annual return. That is a lot — roughly twice the long-term equity market average. The claim is plausible if the investment is aggressive or speculative (startup equity, leveraged property, a specific sector bet). It is implausible if the investment is described as safe (government bonds, savings accounts, balanced funds). A quick Rule of 72 check on any advertised return tells you what rate it implies, which tells you what risk level must be involved.

The compound debt implication

Applied to debt, the rule is sobering. A 29.9% store card compounds a balance to double every 2.4 years. A 22% credit card doubles every 3.3 years. A 35% overdraft doubles every 2 years. In each case, the balance compounds onto itself — meaning by year 6, a 5,000 store card balance has become 20,000 if no payments are made. The same mechanic that grows savings drains debtors faster than intuition suggests. Running the rule on any debt you are carrying makes the urgency of paying it down concrete in a way APR percentages do not.

The one-rate limitation

The rule assumes a constant rate over the doubling period. Real investment returns vary year to year. A portfolio averaging 7% might return 15% some years and -10% others. The Rule of 72 still works on the average, but the path to the average matters for staying patient. Knowing that 7% doubles in 10 years does not help someone panic-selling at year 2 during a 20% drop. The arithmetic is clean; the behaviour required to actually realise the doubling is the hard part.

What the calculator does

The tool applies the Rule of 72 to an interest or growth rate and returns the approximate doubling time. It is a mental-model trainer more than a precise calculator. For exact doubling-time requirements, use the compound interest calculator and solve for t. For quick checks, decision-making, and reality-testing claims, the rule is faster.