Rule of 72 Calculator
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Use the Rule of 72 to estimate doubling time for any interest rate — or find the rate needed to double in a target number of years. Also shows Rules of 115 and 144.
How long to double at common UK savings and investment rates using the Rule of 72:
| Annual Rate | Rule of 72 (years) | Exact formula (years) | Example context |
|---|---|---|---|
| 2% | 36.0 | 35.0 | Low-rate easy-access savings |
| 3% | 24.0 | 23.4 | Moderate savings / inflation |
| 5% | 14.4 | 14.2 | Premium savings accounts 2026 |
| 7% | 10.3 | 10.2 | Stocks & Shares ISA long-term average |
| 10% | 7.2 | 7.3 | High-performing equity funds |
| 15% | 4.8 | 5.0 | Aggressive growth / emerging markets |
| 20% | 3.6 | 3.8 | Credit card debt — works against you |
The Rule of 72 can be extended to estimate tripling and quadrupling times:
| Rule | Constant | Predicts | At 7% |
|---|---|---|---|
| Rule of 72 | 72 | Doubling time | 10.3 years |
| Rule of 115 | 115 | Tripling time | 16.4 years |
| Rule of 144 | 144 | Quadrupling time | 20.6 years |
These constants come from logarithms. To double: ln(2) ÷ r ≈ 0.693 ÷ r. We use 72 instead of 69.3 because 72 has more divisors (2, 3, 4, 6, 8, 9, 12) making mental division easier. Similarly, ln(3) ≈ 1.099 gives the Rule of 110 precisely, and ln(4) = 2×ln(2) ≈ 1.386 gives the Rule of 139 precisely — but 115 and 144 are used as round-number approximations.
The FTSE All-World index has historically returned around 7-8% annually. At 7%, money doubles in 10.3 years. A 30-year-old who invests £20,000 in an ISA today could see it grow to £40,000 by age 40, £80,000 by age 50, and £160,000 by age 60 — three doublings from compound growth alone, before any further contributions.
If your pension grows at 6% real return per year after inflation, it doubles every 12 years. Starting a pension at 25 gives you roughly three doubling periods before state pension age at 67 — multiplying your money approximately eightfold in real terms.
The average UK credit card charges 23-25% APR. At 24% APR, unpaid debt doubles in exactly 3 years. A £3,000 balance ignored for 6 years becomes £12,000 — a fourfold increase. The Rule of 72 makes the danger viscerally clear.
The Rule of 72 is a simple mental maths shortcut to estimate how long it takes an investment to double at a fixed annual rate of return. You divide 72 by the annual interest rate (as a percentage). For example, at 6% per year, 72 ÷ 6 = 12 years to double. It works for compound growth — savings accounts, investments, pensions, or any asset growing at a steady rate. The rule was first described by Italian mathematician Luca Pacioli around 1494.
The Rule of 72 is a very good approximation for rates between about 6% and 10% per year. At exactly 8%, the true doubling time is 9.01 years, while the Rule of 72 gives 9 years — extremely close. At lower rates (2-3%), using 69.3 (the mathematically precise constant for continuous compounding) gives a better estimate. At higher rates (20%+), the rule slightly underestimates doubling time. For everyday financial planning and quick mental calculations, the Rule of 72 is accurate enough.
The Rule of 72 is an approximation based on the mathematical property of natural logarithms. The exact formula for doubling time is T = ln(2) ÷ ln(1 + r), where r is the decimal rate. At 6% annual return, ln(2) ÷ ln(1.06) = 11.896 years, versus 12 years from the Rule of 72 — a difference of just 0.1 years. The rule is excellent for quick estimates; use the exact compound interest formula when precision matters for long-term projections.
Yes — the Rule of 72 applies equally to debt. If you carry a credit card balance at 24% APR, your debt doubles in 72 ÷ 24 = 3 years if you make no payments. At a typical UK personal loan rate of 7%, debt doubles in about 10 years. This is why high-interest debt is so dangerous: compound interest works against you just as powerfully as it works for you with investments. The rule is a stark reminder of the urgency of paying down high-rate debt.
Absolutely. The Rule of 72 works for any compound growth, including inflation. At 3% inflation, the purchasing power of £1 halves in 72 ÷ 3 = 24 years. At 5% inflation, it halves in about 14 years. This is why keeping large amounts in cash long-term erodes wealth: at 3% inflation, a £10,000 emergency fund kept in a 0% current account loses half its real value over 24 years. Earning even 4.5% in a Cash ISA (above inflation) preserves and slightly grows real wealth.