Rule of 70

Technique: Doubling time ≈ 70 / r%

For compound growth at r% per period, the doubling time is approximately 70 / r periods. Run it either direction: given a rate, divide; given a doubling time, divide back.

Examples

• 5% growth → doubles in 70 / 5 = 14 years.
• 10% growth → 70 / 10 = 7 years.
• 2% growth → 70 / 2 = 35 years (the long-run economy).
• Inverse: doubles in 7 years → 70 / 7 = 10% annual.
• Inverse: doubles in 14 years → 70 / 14 = 5%.

Why does this work?

Doubling means (1 + r/100)^t = 2, so t = ln(2) / ln(1 + r/100) ≈ ln(2) / (r/100) for small r. ln(2) ≈ 0.693, so t ≈ 69.3 / r. Round to 70 for mental ease.

For tripling use 110 instead (Rule of 110, since ln(3) ≈ 1.099). For 10x use 230. The Rule of 70 is the workhorse for finance interview questions about doubling capital, population, debt, etc.

This round restricts rates to clean divisors of 70 so every answer is a whole number. Every question has a 30 second shot clock.