A sum of money invested at compound' interest amounts to Rs. 1,000 in 2 years and 1,200 in 3 years. Find the rate of interest.

Given:

Amount (A₂) in 2 years = ₹1,000

Amount (A₃) in 3 years = ₹1,200

Formula used:

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

Where,

P = Principal

r = rate of interest

t = time

Calculation:

Let P be the principal and r be the rate of interest.

For 2 years: 1,000 = P(1 + r/100)²

For 3 years: 1,200 = P(1 + r/100)³

Divide the second equation by the first:

1,200 / 1,000 = (P(1 + r/100)³) / (P(1 + r/100)²)

⇒ 1.2 = (1 + r/100)

⇒ 1 + r/100 = 1.2

⇒ r/100 = 0.2

⇒ r = 20%

∴ The correct answer is option (2).