A woman invests Rs 2000 at the start of each year in a scheme that pays 5% compound interest per annum, compounded yearly. How much will the total value of her investments be at the end of the 2nd year?

Introduction / Context:
This question involves a simple form of recurring investment under compound interest. The woman deposits Rs 2000 at the start of each year, and the investment earns 5% compound interest per annum. We must track each deposit separately, because the first deposit earns interest for 2 years, while the second deposit earns interest for only 1 year by the end of the 2nd year.

Given Data / Assumptions:

• Deposit each time = Rs 2000.
• Interest rate = 5% per annum, compounded yearly.
• First deposit is made at the start of year 1.
• Second deposit is made at the start of year 2.
• We want the total amount at the end of year 2.

Concept / Approach:
Treat each deposit as a separate principal with its own time period. The first deposit earns interest for 2 years, and the second deposit earns interest for 1 year. For each deposit, use the compound interest amount formula:
A = P * (1 + r / 100)^t Then add the resulting amounts together to obtain the total investment value.

Step-by-Step Solution:
First deposit: P1 = 2000, time t1 = 2 years. Amount from first deposit: A1 = 2000 * (1.05)^2. (1.05)^2 = 1.1025, so A1 = 2000 * 1.1025 = Rs 2205. Second deposit: P2 = 2000, time t2 = 1 year. Amount from second deposit: A2 = 2000 * 1.05 = Rs 2100. Total value at end of year 2 = A1 + A2 = 2205 + 2100 = Rs 4305.

Verification / Alternative Check:
Check interest earned on each deposit. First deposit interest = 2205 - 2000 = 205 over 2 years. Second deposit interest = 2100 - 2000 = 100 over 1 year. Total interest = 205 + 100 = 305, added to total deposits of 4000 gives 4305. This matches our calculated total amount.

Why Other Options Are Wrong:
Rs. 430 is far too small and ignores the size of the deposits. Rs. 4355 and Rs. 4350 are slightly larger than the correct value and come from errors in compounding or addition.

Common Pitfalls:
A common mistake is to treat the situation as if Rs 4000 were invested at once for 2 years, which is not accurate here. Some learners mistakenly apply 2 years of interest to both deposits, overestimating the final amount.

Final Answer:
The total value of her investments at the end of the 2nd year is Rs. 4305.