Compound Interest – Effect of increasing the rate: ₹ 400 amounts to ₹ 441 in 2 years at some rate r (annual compounding). If the rate is increased by 5% per annum, what will be the new amount after 2 years?

Introduction / Context:
We first infer the original rate from the known amount, then add 5% to that rate and recompute the 2-year amount.

Given Data / Assumptions:

• 400 grows to 441 in 2 years
• (1 + r)^2 = 441/400 = 1.1025 → 1 + r = 1.05 → r = 5%
• New rate = 5% + 5% = 10%

Concept / Approach:
Amount with new rate: A_new = 400 * (1.10)^2.

Step-by-Step Solution:
A_new = 400 * 1.21 = ₹ 484

Verification / Alternative check:
Original A = 400 * 1.1025 = 441 (checks), so r = 5% is correct before adding 5%.

Why Other Options Are Wrong:
₹ 560, ₹ 512, ₹ 600 correspond to higher rates or extra years.

Common Pitfalls:
Adding 5% to the amount instead of the rate, or applying simple interest.

Final Answer:
₹ 484