Estimate how long it takes your investment to double
The Rule of 72 is one of the most elegant shortcuts in finance. It allows you to estimate how long it will take for an investment to double in value by simply dividing 72 by the annual interest rate. No logarithms, no spreadsheets, just quick mental arithmetic. Despite its simplicity, it is remarkably accurate for interest rates commonly encountered in savings accounts, bonds, and equity markets. This rule has been used by investors, bankers, and financial advisors for centuries. Its origins trace back to at least 1494, when Italian mathematician Luca Pacioli referenced it in his work "Summa de Arithmetica". The enduring popularity of the Rule of 72 speaks to its practical value. In a world of complex financial products and volatile markets, being able to quickly estimate doubling time gives investors a powerful intuitive tool for comparing opportunities. The calculator below computes both the Rule of 72 approximation and the exact result using the logarithmic formula. This lets you see precisely how close the approximation is at any given rate. For UK investors evaluating Cash ISA rates, workplace pension growth, or equity index fund returns, this comparison provides useful context for setting realistic expectations about long-term wealth accumulation.
To use the Rule of 72 calculator: 1. Select your calculation mode. "Years to double" takes an interest rate and tells you how many years until your investment doubles. "Required rate to double" takes a target number of years and tells you what annual return you need. 2. For "Years to double" mode, enter the expected annual interest rate as a percentage. This could be a savings account rate, an average equity return, or a bond yield. The calculator will show both the Rule of 72 estimate and the exact result. 3. For "Required rate to double" mode, enter the number of years in which you want your money to double. The calculator will tell you what annual return rate is needed to achieve that goal. 4. Review the approximation error to see how close the Rule of 72 is to the exact answer. At rates near 8%, the error is typically less than 0.5%. At very low or very high rates, the approximation becomes less precise.
The Rule of 72 formula is straightforward: Years to Double = 72 / Annual Interest Rate (%) For example, at 6% annual growth: 72 / 6 = 12 years to double. The exact formula uses logarithms: Precise Years = ln(2) / ln(1 + r) Where r is the annual rate as a decimal (e.g. 0.06 for 6%). For the reverse calculation (required rate): Required Rate = 72 / Target Years (Rule of 72) Precise Rate = (2^(1/n) - 1) x 100 (exact formula) The Rule of 72 works because ln(2) is approximately 0.693, and for small values of r, ln(1+r) is approximately r. The number 72 was chosen instead of 69.3 (which would be more mathematically precise) because 72 has many divisors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), making mental arithmetic easier. The approximation error is calculated as: Error = |Rule of 72 Result - Exact Result| / Exact Result x 100% For rates between 2% and 20%, the error is typically under 3%, making the Rule of 72 a reliable quick estimate for most practical investment scenarios.
The Rule of 72 has several practical applications for UK investors. When comparing Cash ISA rates, you can quickly determine that a 4% rate will double your money in about 18 years, while a 2% rate takes 36 years. For equity investors, the FTSE All-Share index has historically returned roughly 7-8% annually including dividends, suggesting a doubling period of about 9-10 years in nominal terms. Remember that the Rule of 72 works with nominal returns. To estimate real (inflation-adjusted) doubling time, subtract the inflation rate from your nominal return before dividing into 72. With 7% nominal returns and 2.5% inflation, your real rate is roughly 4.5%, giving a real doubling time of about 16 years. For a more precise calculation of inflation-adjusted returns, use our Real Return Calculator. The Rule of 72 can also be applied in reverse to understand the impact of fees. A 1% annual management fee on a fund effectively increases the doubling time. Compare: at 7% gross return, doubling takes about 10.3 years; at 6% net return (after 1% fee), it takes 12 years. Over a 40-year career, that difference compounds significantly.