A sum of money with compound interest becomes Rs. 400 in 2 years and Rs. 500…

CONCEPT: In compound interest, the amount is multiplied by the same annual growth factor each year when the rate is constant.

If the one-year factor is R, then the amount after two years is P × R2, where P is the original sum.

APPLICATION:

1. From year 2 to year 3, the one-year factor is R = 500 ÷ 400 = 1.25 because the amount rises from ₹400 to ₹500 in one year.

2. The two-year amount is ₹400, so P × R2 = 400.

3. Substitute R = 1.25: P = 400 ÷ 1.252.

4. Since 1.252 = 1.5625, P = 400 ÷ 1.5625 = 256.

CROSS-CHECK:

₹256 × 1.25 × 1.25 = ₹400, and one more multiplication by 1.25 gives ₹500, so the given amounts are matched.

Result: The original sum is ₹256.