A machine depreciates by 10% per year. If its present value is Rs. 4000, what will be its value after 2 more years?

Introduction / Context: Depreciation compounded annually reduces value by a fixed fraction each year. After n years at rate r, value multiplies by (1 − r)^n. Apply this to the current value to get the future value after more depreciation.

Given Data / Assumptions:

• Current value V = ₹4000.
• Annual depreciation rate = 10% ⇒ factor 0.90 per year.
• Time = 2 years.

Concept / Approach: Future value after 2 years: V * (0.90)^2. Compute exactly to avoid rounding errors: 0.9^2 = 0.81.

Step-by-Step Solution:

Verification / Alternative check: Year 1: 4000 → 3600. Year 2: 3600 → 3240. Same outcome.

Why Other Options Are Wrong: ₹3200 and ₹3280 reflect linear changes instead of compounded; ₹3260 is a rounding guess; ₹3000 is too low.

Common Pitfalls: Subtracting 20% once instead of compounding 10% twice, or subtracting 10 percentage points of the original value each year.

Final Answer: Rs. 3240