A sum of ₹ 3,000 amounts to ₹ 6,000 in two years at compound interest. The interest for four years is 

Given:

Principal (P) = ₹3,000

Amount (A) = ₹6,000

Time (t) = 2 years

Formula used:

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

Where, r = rate

Calculations:

6000 = 3000(1 + r/100)²

⇒ 2 = (1 + r/100)²

⇒ √2 = 1 + r/100

⇒ r/100 = √2 - 1

⇒ r = (√2 - 1) × 100

⇒ r ≈ 41.42%

Now, for 4 years:

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

A = 3000(1 + 0.4142)⁴

A = 3000(1.4142)⁴

A ≈ 3000 × 4.000

A ≈ 12,000

Interest for 4 years = A - P

Interest for 4 years = 12,000 - 3,000

Interest for 4 years = 9,000

∴ The correct answer is option 4.

Shortcut Trick P = 3000

Amount = 6000

We can say that,

In 2 years, amount becomes 2 times

   × 2                                      × 2

In 4 years, amount becomes 4 times

So amount in 4 years = 4 × 3000 = 12000

Interest = Amount - Principal = 12000 - 3000 = 9000

∴ The correct answer is 9000.