✨ Rule of 72 Calculator
Quickly estimate how long it takes to double your money. Compare 72 rule vs exact calculation, multi-billion, and inflation impact.
Mode
DCA Doubling
Doubling Time
10.29 yr
Multiples of Money
2×
10.29 yr
10.24 yr
3×
16.29 yr
16.24 yr
4×
20.57 yr
20.49 yr
10×
34.29 yr
34.03 yr
Rate Sensitivity
| Rate | Rule Estimate | Exact Years | Error |
|---|---|---|---|
| 2% | 36yr | 35yr | 1yr |
| 4% | 18yr | 17.67yr | 0.33yr |
| 6% | 12yr | 11.9yr | 0.1yr |
| 8% | 9yr | 9.01yr | 0.01yr |
| 10% | 7.2yr | 7.27yr | 0.07yr |
| 12% | 6yr | 6.12yr | 0.12yr |
| 14% | 5.1yr | 5.29yr | 0.15yr |
| 16% | 4.5yr | 4.67yr | 0.17yr |
| 18% | 4yr | 4.19yr | 0.19yr |
| 20% | 3.6yr | 3.8yr | 0.2yr |
| 22% | 3.3yr | 3.49yr | 0.21yr |
| 24% | 3yr | 3.22yr | 0.22yr |
| 26% | 2.8yr | 3yr | 0.23yr |
| 28% | 2.6yr | 2.81yr | 0.24yr |
| 30% | 2.4yr | 2.64yr | 0.24yr |
Accuracy Analysis
🔥 At 3% inflation, purchasing power halves in 24 years
How It Works
Rule of 72 Formula
Years to Double = 72 ÷ Rate(%)
Mathematical Derivation
The Rule of 72 comes from the Taylor series expansion: ln(1+r) ≈ r - r²/2 + r³/3 - ... For small r, ln(1+r) ≈ r So doubling time = ln(2)/ln(1+r) ≈ 0.693/r = 69.3/r ≈ 72/r (adjusted for practicality)
Example
• At 7% return: Rule of 72 says 72÷7 ≈ 10.3 years. Exact: ln(2)/ln(1.07) ≈ 10.24 years. Error: 0.06 years.
• Inflation at 3%: purchasing power halves in 72÷3 = 24 years.
• To double money in 6 years: need 72÷6 = 12% annual return.
❓ FAQ
What is the Rule of 72?＋
The Rule of 72 is a quick mental math shortcut to estimate how long it takes an investment to double. Divide 72 by the annual return rate. At 8%, money doubles in ~9 years.
How accurate is the Rule of 72?＋
Very accurate for rates between 6-10%. At 1% error is ~4%, at 20% error is ~15%. For precise calculations, use ln(2)/ln(1+r). Our calculator shows both.
Why 72 and not other numbers?＋
72 is divisible by many numbers (1,2,3,4,6,8,9,12...) making mental math easy. 69.3 is more mathematically precise (continuous compounding). 72 is practical for discrete annual compounding.
Can I use the Rule of 72 for inflation?＋
Yes! At 3% inflation, 72÷3 = 24 years for purchasing power to halve. Use our inflation mode for this calculation.
What about tripling or quadrupling money?＋
Use Rule of 114 for tripling (114÷rate) and Rule of 144 for quadrupling (144÷rate). Our calculator handles all multiples.
Does the Rule of 72 work for debt?＋
Yes. At 18% credit card APR, debt doubles in 72÷18 = 4 years if unpaid. This shows how dangerous high-interest debt can be.
How does continuous compounding change the rule?＋
For continuous compounding, use 69.3 instead of 72. ln(2) ≈ 0.693, so doubling time = 69.3÷rate. Our calculator shows both discrete and continuous versions.
What's the relationship to CAGR?＋
CAGR is the actual annualized return. The Rule of 72 gives a quick estimate. For precise CAGR, use our Compound Interest or Investment Return calculators.