A woman invests Rs. 200 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. 431
B. `430.5`
C. 435
D. 430

Answer

To solve the problem step-by-step, we need to calculate the total amount of investment at the end of the second year, considering the compound interest.

### Step 1: Calculate the amount from the first year's investment
The woman invests Rs. 200 at the beginning of the first year. This amount will earn compound interest for 2 years at a rate of 5%.

The formula for compound interest is:
\[ A = P(1 + r)^n \]
where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = principal amount (the initial amount of money).
- \( r \) = annual interest rate (decimal).
- \( n \) = number of years the money is invested or borrowed.

For the first investment:
- \( P = 200 \)
- \( r = 5\% = 0.05 \)
- \( n = 2 \)

Substituting the values into the formula:
\[ A = 200(1 + 0.05)^2 \]
\[ A = 200(1.05)^2 \]
\[ A = 200 \times 1.1025 \]
\[ A = 220.5 \]

### Step 2: Calculate the amount from the second year's investment
The woman invests another Rs. 200 at the beginning of the second year. This amount will earn interest for 1 year at the same rate of 5%.

For the second investment:
- \( P = 200 \)
- \( r = 5\% = 0.05 \)
- \( n = 1 \)

Substituting the values into the formula:
\[ A = 200(1 + 0.05)^1 \]
\[ A = 200(1.05) \]
\[ A = 200 \times 1.05 \]
\[ A = 210 \]

### Step 3: Calculate the total amount at the end of the second year
Now, we add the amounts from both investments:
- Amount from the first investment after 2 years: Rs. 220.5
- Amount from the second investment after 1 year: Rs. 210

Total amount:
\[ \text{Total Amount} = 220.5 + 210 = 430.5 \]

Thus, the total investment at the end of the second year is **Rs. 430.5**.