The Rule of 72

Why 72?

The exact answer uses natural logarithms: doubling time = ln(2) / ln(1 + r), which is roughly 0.693 / r for small r. The constant 72 was chosen because it's close to 69.3 and has many integer factors (2, 3, 4, 6, 8, 9, 12), making mental division easy.

The rule is most accurate at about 8%. At lower rates (2–4%) use 69 for better precision; at higher rates (15–20%) use 75.

Practical uses

Sanity-checking claims. When someone promises "we can double your money in five years," the implied rate is 72/5 ≈ 14.4% per year. That's a specific, aggressive claim — evaluate it accordingly.

Choosing retirement savings rates. If you're 35 with $100,000 saved and want $800,000 by age 65, you need three doublings in 30 years — one every 10 years — which requires about 7.2% after-inflation returns. That's achievable but not guaranteed.

Understanding inflation damage. At 3% inflation, purchasing power halves every 24 years (72 ÷ 3). A dollar in 2026 is worth about 50 cents in 2050.

Related: Rule of 114 and Rule of 144

The same idea scales to other multiples:

• Rule of 114 — years to triple your money (114 ÷ rate).
• Rule of 144 — years to quadruple (144 ÷ rate).

At 8%, money triples in about 14 years and quadruples in about 18 years.

Limits

The Rule of 72 assumes a constant rate of return. Real markets don't behave that way — they compound at a noisy average with years of loss interrupting the doubling. The rule gives you an accurate answer for the average path; the actual path is bumpier.

How Horizons uses this

Horizons doesn't use the Rule of 72 directly — it compounds every asset every month at strategy-specific rates. But the rule is a useful way to sanity-check what the engine shows you. If your portfolio is projected to grow from $500k to $2M over 20 years, that's two doublings, which the rule translates to about 7.2% annual return — a reasonable long-run expectation for a moderate-to-aggressive portfolio.