A woman invests Rs. 4000 at the start of each year at 5% compound interest per annum. How much will her investment be at the end of the `2^(nd)` year?

Options

A. Rs. 8601
B. Rs. 8615
C. Rs. 8600
D. Rs. 8610

Answer

To solve the problem, we need to calculate the total amount of investment at the end of the second year, considering that the woman invests Rs. 4000 at the start of each year at a compound interest rate of 5% per annum.

### Step-by-Step Solution:

1. **Calculate the amount from the first investment (Year 1):**
- The first investment of Rs. 4000 is made at the start of the first year.
- This amount will compound for 2 years.
- The formula for compound interest is:
\[ A = P(1 + r)^n \]
where \( A \) is the amount after time \( n \), \( P \) is the principal amount, \( r \) is the rate of interest, and \( n \) is the number of years.
- Here, \( P = 4000 \), \( r = 0.05 \), and \( n = 2 \).
- Substituting the values:
\[ A_1 = 4000(1 + 0.05)^2 = 4000(1.05)^2 = 4000 \times 1.1025 = 4410 \]

2. **Calculate the amount from the second investment (Year 2):**
- The second investment of Rs. 4000 is made at the start of the second year.
- This amount will compound for 1 year.
- Using the same formula:
- Here, \( P = 4000 \), \( r = 0.05 \), and \( n = 1 \).
- Substituting the values:
\[ A_2 = 4000(1 + 0.05)^1 = 4000(1.05) = 4000 \times 1.05 = 4200 \]

3. **Calculate the total amount at the end of the second year:**
- Now, we add the amounts from both investments:
\[ \text{Total Amount} = A_1 + A_2 = 4410 + 4200 = 8610 \]

### Final Answer:
The total amount of her investment at the end of the second year will be Rs. 8610.