A certain sum becomes 3 times itself in 4 years at compound interest. The number of years in which it becomes 27 times itself is

Given:

A certain sum becomes 3 times itself in 4 years at compound interest.

Find the number of years in which it becomes 27 times itself.

Formula used:

Amount (A) = Principal (P) × (1 + r)^t

Where,

A/P = (1 + r)^t

Calculation:

Given: A = 3P, t = 4 years

⇒ 3 = (1 + r)⁴

⇒ (1 + r) = 3^1/4

Now, for A = 27P, find t:

⇒ 27 = (1 + r)^t

⇒ 27 = (3^1/4)^t

⇒ 27 = 3^t/4

⇒ 3³ = 3^t/4

⇒ t/4 = 3

⇒ t = 3 × 4

⇒ t = 12 years

∴ The correct answer is option (3).