What is the least number of complete years for a sum to more than double at 20% compound interest per annum?

Problem restatement
Find the smallest integer n such that (1 + 0.20)ⁿ > 2.

Given data

• Annual compound rate r = 20% = 0.20
• Target: amount factor > 2

Concept/Approach
Test integer years until the compound factor exceeds 2.

Step-by-step calculation
(1.2)³ = 1.728 < 2(1.2)⁴ = 2.0736 > 2Least n = 4

Verification/Alternative
Using logs: n > log 2 ÷ log 1.2 ≈ 0.3010 ÷ 0.07918 ≈ 3.80 → next integer 4.

Common pitfalls
Comparing to 2.0 after only 3 years (still short).

Final Answer
4 years