The amount of money appreciates to ₹ 700 after 4 years and to ₹ 1000 after 8 years at a certain compound interest compounded annually. The initial amount of money was

Given:

Amount after 4 years (A1) = ₹700

Amount after 8 years (A2) = ₹1000

Formula used:

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

Where,

P = Principal amount

r = Rate of interest

t = Time period

Calculation:

700 = P(1 + r/100)⁴     ...(1)

1000 = P(1 + r/100)⁸     ...(2)

Dividing (2) by (1):

⇒ 1000 / 700 = (P(1 + r/100)⁸) / (P(1 + r/100)⁴)

⇒ 10 / 7 = (1 + r/100)⁴

Let (1 + r/100) = x

⇒ (10/7) = x⁴

⇒ x = (10/7)^1/4

Using (1):

700 = P × (10/7)^{1/4 × 4}

⇒ 700 = P × (10/7)

⇒ P = 700 × 7 / 10

⇒ P = 490

∴ The correct answer is option 1.