If the interest is compounded half-yearly, calculate the amount when principal is Rs 7,400, the rate of interest is 5% per annum and the duration is one year.

Answer

To solve the problem of calculating the amount when the principal is Rs 7,400, the rate of interest is 5% per annum, and the duration is one year with interest compounded half-yearly, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Principal (P) = Rs 7,400
- Rate of Interest (R) = 5% per annum
- Time (T) = 1 year

2. **Convert the Rate for Half-Yearly Compounding**:
Since the interest is compounded half-yearly, we need to adjust the rate and time:
- Half-yearly Rate (R/2) = 5% / 2 = 2.5%
- Number of Compounding Periods (N) = 2 (since there are two half-year periods in one year)

3. **Use the Compound Interest Formula**:
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100n}\right)^{nt} \]
Here, \( n \) is the number of times interest is compounded per year. For half-yearly compounding, \( n = 2 \).

Plugging in the values:
\[ A = 7400 \left(1 + \frac{2.5}{100}\right)^{2} \]

4. **Calculate the Amount**:
- Calculate \( 1 + \frac{2.5}{100} = 1 + 0.025 = 1.025 \)
- Now, raise this to the power of 2:
\[ A = 7400 \times (1.025)^{2} \]
- Calculate \( (1.025)^{2} = 1.050625 \)
- Now multiply by the principal:
\[ A = 7400 \times 1.050625 = 7774.625 \]

5. **Final Result**:
The amount after 1 year when compounded half-yearly is:
\[ A = Rs 7774.625 \]