A woman invests Rs. 2,000 at the start of each year at 5% compound interest per annum. Assuming the first Rs. 2,000 is invested for 2 full years and the second Rs. 2,000 is invested for 1 full year, how much will the total value of her investments be at the end of the 2nd year?

Introduction:
This is an example of an annuity due type problem where equal amounts are invested at the start of each year and earn compound interest for different lengths of time. The question tests the ability to handle multiple deposits with varying investment periods under the same interest rate.

Given Data / Assumptions:
First investment = Rs. 2,000 at the start of year 1. Second investment = Rs. 2,000 at the start of year 2. Rate of compound interest = 5% per annum. Interest is compounded annually. We need the total value at the end of year 2.

Concept / Approach:
The first deposit earns interest for 2 years, while the second deposit earns interest for only 1 year by the time we reach the end of year 2. We treat each deposit separately using the compound interest amount formula: A = P * (1 + r/100)^n for the appropriate n, and then sum the two resulting amounts.

Step-by-Step Solution:
Step 1: Compute the value of the first deposit. P₁ = 2000, n₁ = 2 years, r = 5%. A₁ = 2000 * (1.05)^2 = 2000 * 1.1025 = Rs. 2,205. Step 2: Compute the value of the second deposit. P₂ = 2000, n₂ = 1 year. A₂ = 2000 * 1.05 = Rs. 2,100. Step 3: Total value at the end of year 2. Total amount = A₁ + A₂ = 2,205 + 2,100 = Rs. 4,305.

Verification / Alternative check:
We can reason that the total investment is Rs. 4,000 and that average holding time is between 1 and 2 years, so the total should be somewhat above Rs. 4,200. The computed Rs. 4,305 is consistent with this expectation and matches the precise calculation using the multipliers 1.1025 and 1.05.

Why Other Options Are Wrong:
Rs. 430 is far too small, clearly missing the principal amount. Rs. 4,355 and Rs. 4,350 represent small arithmetic errors or incorrect exponents. Rs. 4,205 ignores part of the compounding or miscalculates one year of interest.

Common Pitfalls:
Many students mistakenly treat both amounts as if they were invested for 2 years or both for 1 year. Another mistake is to add Rs. 4,000 and then calculate interest on that total for some arbitrary time. The correct method is to treat each cash flow separately with its appropriate time period.

Final Answer:
At the end of the 2nd year, her investments will be worth Rs. 4,305 in total.