Finance⏱ 4 min read
What Is the Rule of 72 and How Accurate Is It?
The Rule of 72 is the fastest way to estimate how long any investment takes to double. Here's the formula, where it comes from, and exactly how accurate it is across different interest rates.
The Rule of 72 is one of the most useful mental maths shortcuts in finance. It gives a quick answer to the question "how long until my money doubles?" without needing a calculator.
The Rule
Years to double = 72 ÷ Annual interest rate (%)
At 6%: 72 ÷ 6 = 12 years
At 8%: 72 ÷ 8 = 9 years
At 4%: 72 ÷ 4 = 18 years
At 12%: 72 ÷ 12 = 6 years
At 2%: 72 ÷ 2 = 36 years
Where 72 Comes From
The exact doubling time from compound interest is:
Exact years to double = ln(2) ÷ ln(1 + r)
Where ln = natural logarithm and r = decimal rate
For small r: ln(1 + r) ≈ r
So years ≈ ln(2) ÷ r = 0.6931 ÷ r
Multiplying top and bottom by 100:
= 69.31 ÷ r%
72 works better than 69.31 in practice because:
- It's easier to divide (more factors: 2, 3, 4, 6, 8, 9, 12...)
- It slightly overestimates at typical rates (5–10%), which is a useful conservative bias
Accuracy Across Different Rates
Interest RateRule of 72 EstimateExact AnswerError
2%36 years35.0 years+2.8%
5%14.4 years14.2 years+1.7%
8%9.0 years9.0 years0%
10%7.2 years7.27 years−1.0%
15%4.8 years4.96 years−3.4%
25%2.88 years3.11 years−8.0%
The rule is most accurate between 5–10% — exactly the range relevant for most investment decisions. It becomes less accurate at very high or very low rates.
The Rule of 72 in Reverse
Implied rate = 72 ÷ Years to double
Your investment doubled in 7 years:
Implied rate ≈ 72 ÷ 7 = 10.3% per year
Property bought for £200k, worth £400k after 12 years:
Implied rate ≈ 72 ÷ 12 = 6% per year
Applying the Rule to Inflation (and Debt)
Inflation at 4%: purchasing power halves in 72÷4 = 18 years
Your £100,000 in cash under the mattress at 4% inflation:
In 18 years, it's worth the equivalent of only £50,000 today.
Debt at 20% APR: balance doubles in 72÷20 = 3.6 years
A £3,000 credit card debt left unpaid doubles to £6,000 in ~3.5 years.
Variants: Rule of 70 and Rule of 69.3
- Rule of 70: Better for very low rates (1–3%), particularly inflation calculations
- Rule of 69.3: Most mathematically precise for continuously compounded interest
- Rule of 72: Best for typical investment rates (5–10%) and mental arithmetic