FinanceCalcs
Rule of 72 Calculator
Estimate how long it takes to double your money at any interest rate — or find the rate required to double in a target number of years — using the Rule of 72 mental math shortcut.
Works for investments, savings accounts, debt, and inflation — with an exact doubling calculation alongside the Rule of 72 estimate.
Rule of 72 Calculator
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"Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it."
— Often attributed to Albert Einstein
How the Rule of 72 works
The Rule of 72 is a mental math shortcut for estimating how long it takes to double money at a given compound growth rate. Divide 72 by the annual interest rate and you get an approximate doubling time in years. At an 8% annual return, money doubles in roughly 72 ÷ 8 = 9 years. At 6%, it takes about 12 years. At 12%, just 6 years.
The rule also works in reverse: divide 72 by the number of years you want to double in, and you get the required annual rate. Want to double in 6 years? You need roughly 72 ÷ 6 = 12% annual return.
Crucially, the rule applies just as powerfully to debt and inflation — both of which compound against you. At 18% credit card interest, your balance doubles in about 4 years. At 3% inflation, purchasing power is cut in half in roughly 24 years. Understanding compounding in both directions is one of the most useful concepts in personal finance.
lightbulb Rule of 72 in Action
Investing: You invest $20,000 in a diversified index fund averaging 7% annually. Rule of 72 estimate: doubles in 72 ÷ 7 ≈ 10.3 years. Exact answer: 10.24 years. At that rate, $20,000 becomes ~$40,000 in about a decade — and ~$80,000 in two decades.
Debt: You carry a $5,000 credit card balance at 24% APR and make no payments. Your balance doubles in roughly 72 ÷ 24 = 3 years — reaching $10,000 by year three.
Inflation: At a 3% inflation rate, the purchasing power of $100,000 in savings is halved in roughly 72 ÷ 3 = 24 years — meaning it buys only $50,000 worth of goods in today's dollars by 2048.
The Rule of 72 turns abstract percentages into concrete timelines — making the power (and danger) of compounding immediately intuitive.
Rule of 72 Calculator FAQs
How accurate is the Rule of 72?
Very accurate for typical investment rates between 6% and 10%, where the error is less than 0.1 years. Accuracy declines at very low rates (below 3%) or very high rates (above 20%). The Rule of 70 is slightly more accurate at low rates; the Rule of 69.3 is the most mathematically precise approximation. For everyday planning, the Rule of 72 is accurate enough and far easier to calculate mentally.
Can the Rule of 72 be used for inflation?
Yes — and this is one of its most sobering applications. Divide 72 by the inflation rate to find how long it takes for prices to double (or equivalently, for the purchasing power of cash savings to be cut in half). At a 3% average inflation rate, purchasing power halves in about 24 years. This is why keeping large amounts of cash uninvested for decades carries its own significant financial risk.
Why is 72 used instead of 70 or 69?
72 is chosen primarily because it is highly divisible — it divides evenly by 1, 2, 3, 4, 6, 8, 9, 12, and 18, making mental arithmetic easy for the most common interest rates. The Rule of 70 is slightly more accurate at low rates, and 69.3 (which equals 100 × ln(2)) is the mathematically exact base — but 72 strikes the best balance of accuracy and practical usability.
Does the Rule of 72 work for monthly compounding?
The Rule of 72 is designed for annual compounding. For monthly compounding, the effective annual rate will be slightly higher than the nominal rate, which shortens the true doubling time modestly. For most practical purposes, using the nominal annual rate with the Rule of 72 gives a close enough estimate — the difference at typical savings or investment rates is usually less than a few months.
Rule of 72 terminology
Doubling Time
The time required for a quantity to double at a constant compound growth rate. Applies equally to investments growing in your favor and to debt or inflation compounding against you.
Rule of 72 vs. Rule of 70
The Rule of 70 uses 70 as the numerator and is slightly more accurate at lower rates (1–3%). The Rule of 72 is more accurate at typical investment rates (6–10%) and is preferred in practice because 72 is divisible by more whole numbers, making mental math simpler.
Compound Annual Growth Rate (CAGR)
The rate at which an investment grows each year, assuming returns are reinvested. CAGR is the rate used in the Rule of 72 formula — the higher the CAGR, the faster money doubles.
Exact Doubling Formula
Years = ln(2) ÷ ln(1 + r), where r is the annual rate as a decimal. This produces the precise doubling time — the Rule of 72 is a practical approximation of this exact formula.
Purchasing Power
The real-world value of money — how much it can actually buy. Inflation erodes purchasing power over time, and the Rule of 72 can be applied to inflation to estimate how long it takes for purchasing power to be cut in half.
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