Rule of 72 Calculator

The Rule of 72 is a mental arithmetic shortcut for estimating how long it takes an investment to double at a given compound annual growth rate. The formula is: Years to Double = 72 / Annual Rate (as a whole number). At 6% growth, money doubles in approximately 72 / 6 = 12 years. At 8%, it doubles in 72 / 8 = 9 years. The rule is most accurate for rates between 2% and 15%.

The mathematical basis is the natural logarithm: the exact doubling time is ln(2) / ln(1 + r), which equals 0.693 / ln(1 + r). For small rates, ln(1 + r) approximates to r, giving 0.693 / r, or roughly 69.3 / r%. The number 72 is used instead of 69.3 because it has more factors (divisible by 2, 3, 4, 6, 8, 9, 12) making mental division easier, and the slight overestimate partially compensates for the approximation error.

The rule also works in reverse: if you want to double your money in a specific number of years, divide 72 by the years to get the required rate. To double in 10 years, you need 72 / 10 = 7.2% annual growth. The rule applies equally to inflation erosion: at 3% inflation, the cost of living doubles every 72 / 3 = 24 years, meaning your £1 buys only 50p worth of today's goods.

The Rule of 72 explained. Years to double money = 72 ÷ annual interest rate. At 6% interest: 72 ÷ 6 = 12 years to double. At 9%: 8 years. At 12%: 6 years. Works for any compounding scenario: savings, investments, debt growth, inflation impact. Accuracy: very good for rates 4-12%. Less accurate above 15% (use Rule of 70 for more precision; Rule of 69.3 mathematically exact). UK practical application: pension projections, mortgage payoff times, inflation erosion.

UK practical examples. 5% savings: doubles every 14.4 years. £10,000 at 5% becomes £20k in 14 years, £40k in 28, £80k in 42. 7% S&P 500 historic real return: doubles every 10.3 years. £20,000 ISA at 7% real: becomes £40k in 10 years, £80k in 20, £160k in 30 years. UK 3% average inflation: money's purchasing power HALVES every 24 years. £100,000 in 1995 has buying power of ~£50,000 in 2024. Cash 2% interest after 3% inflation = −1% real: £10,000 loses £1,000 purchasing power every 5 years.

Rule of 72 for debt growth. Credit card 22% APR (2026): debt doubles every 3.3 years if unpaid. £3,000 debt + only minimum payments = £6,000 in 3 years, £12,000 in 6. Mortgage 5%: doubles every 14 years if interest-only — concerning for long-term IO products. Buy Now Pay Later (BNPL) penalty rate 36%: debt doubles every 2 years. Why Rule of 72 motivates debt repayment — visualises the cost of inaction.

Compound interest visualisation. Albert Einstein reputedly called compound interest 'the eighth wonder of the world' (though attribution disputed). Pension example: £100/month invested age 25-65 at 7%: £262,481 at retirement (contributed £48,000). Same £100/month started age 35: £121,997 (contributed £36,000). Just 10 more years of compounding doubles the final pot. Start early — even £25/month from 22 outperforms £100/month from 35.

Limitations of Rule of 72. Assumes constant returns — real markets fluctuate. Assumes annual compounding — monthly or daily compounding slightly more favourable. Doesn't account for: contributions added each year (use future value formula instead); fees and taxes (UK ISA tax-free but platform fees 0.2-1% reduce growth); inflation (real returns matter more than headline). Better tool: future value calculators that include all variables. Rule of 72 is mental shorthand for quick estimation only.