A woman invests Rs. 100 at the start of each year at 5% compound interest per annum. How much her investment be, at the end of the `2^(nd)` year?

Options

A. Rs. 215.25
B. Rs. 215.5
C. Rs. 215
D. Rs. 215.75

Answer

To solve the problem of how much the woman's investment will be at the end of the 2nd year when she invests Rs. 100 at the start of each year at a 5% compound interest rate, we can follow these steps:

### Step 1: Calculate the amount at the end of the first year.
- **Principal (P)** for the first year = Rs. 100
- **Rate (R)** = 5%
- **Time (n)** = 1 year

Using the compound interest formula:
\[ \text{Amount} = P \times \left(1 + \frac{R}{100}\right)^n \]
Substituting the values:
\[ \text{Amount} = 100 \times \left(1 + \frac{5}{100}\right)^1 \]
\[ = 100 \times (1 + 0.05)^1 \]
\[ = 100 \times 1.05 = 105 \]

### Step 2: Calculate the total amount at the start of the second year.
At the start of the second year, the total amount will include the amount from the first year plus the new investment of Rs. 100:
\[ \text{Total Amount at the start of 2nd year} = 105 + 100 = 205 \]

### Step 3: Calculate the amount at the end of the second year.
- **Principal (P)** for the second year = Rs. 205 (the total amount at the start of the second year)
- **Rate (R)** = 5%
- **Time (n)** = 1 year

Using the compound interest formula again:
\[ \text{Amount} = P \times \left(1 + \frac{R}{100}\right)^n \]
Substituting the values:
\[ \text{Amount} = 205 \times \left(1 + \frac{5}{100}\right)^1 \]
\[ = 205 \times (1 + 0.05)^1 \]
\[ = 205 \times 1.05 = 215.25 \]

### Final Answer:
The total investment at the end of the 2nd year will be **Rs. 215.25**.

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