What is the least number of complete years in which a sum of money put out at 20% compound interest (compounded annually) will be more than doubled?

Given:

Rate of Interest (r) = 20%

Amount (A) = 2 × Principal (P)

Formula used:

A = P(1 + r/100)^t

Calculation:

2P = P(1 + 20/100)^t

⇒ 2 = (1 + 0.2)^t

⇒ 2 = (1.2)^t

Now, we calculate t for different values:

For t = 2, (1.2)² = 1.44

For t = 3, (1.2)³ = 1.728

For t = 4, (1.2)⁴ = 2.0736

⇒ At t = 4, the amount exceeds double the principal.

∴ The least number of complete years is 4, and the correct answer is option (3).