Sita deposited `Rs. 5,000` at `10%` simple interest for 2 years. How much more money will Sita have in her account at the end of two years, if it is compounded semiannually.

Options

A. `Rs. 50 `
B. `Rs. 40 `
C. `Rs. 77.50 `
D. `Rs. 85.50 `

Answer

To solve the problem, we need to calculate the total amount Sita would have at the end of 2 years with both simple interest and compound interest (compounded semiannually). Then, we will find the difference between the two amounts.

### Step 1: Calculate the amount with Simple Interest

The formula for calculating the amount \( A \) with simple interest is:

\[ A = P + SI \]

Where:
- \( P \) = Principal amount (initial deposit)
- \( SI \) = Simple Interest

The formula for Simple Interest \( SI \) is:

\[ SI = \frac{P \times r \times t}{100} \]

Where:
- \( r \) = Rate of interest per annum
- \( t \) = Time in years

Given:
- \( P = 5000 \)
- \( r = 10\% \)
- \( t = 2 \)

Calculating \( SI \):

\[ SI = \frac{5000 \times 10 \times 2}{100} = \frac{100000}{100} = 1000 \]

Now, we can find the total amount \( A \):

\[ A = 5000 + 1000 = 6000 \]

### Step 2: Calculate the amount with Compound Interest (Compounded Semiannually)

The formula for calculating the amount \( A \) with compound interest is:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Where:
- \( n \) = Number of times interest is compounded per year

Given:
- \( P = 5000 \)
- \( r = 10\% = 0.10 \)
- \( t = 2 \)
- \( n = 2 \) (since it is compounded semiannually)

Substituting the values into the formula:

\[ A = 5000 \left(1 + \frac{0.10}{2}\right)^{2 \times 2} \]

Calculating:

\[ A = 5000 \left(1 + 0.05\right)^{4} = 5000 \left(1.05\right)^{4} \]

Calculating \( (1.05)^{4} \):

\[ (1.05)^{4} \approx 1.21550625 \]

Now substituting back:

\[ A \approx 5000 \times 1.21550625 \approx 6077.53 \]

### Step 3: Calculate the difference

Now, we find how much more money Sita will have with compound interest compared to simple interest:

\[ \text{Difference} = A_{\text{compound}} - A_{\text{simple}} = 6077.53 - 6000 \approx 77.53 \]

### Final Answer

Sita will have approximately Rs. 77.53 more in her account at the end of 2 years if the interest is compounded semiannually.

---