Rs. 7500 is borrowed at Cl at the rate of 4% per annum. What will be the amount to the paid after 6 months, if interest is compounded quarterly ?

Answer

To solve the problem of calculating the amount to be paid after 6 months for a loan of Rs. 7500 at a compound interest rate of 4% per annum, compounded quarterly, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Principal (P) = Rs. 7500
- Annual Interest Rate (R) = 4%
- Time (T) = 6 months = 0.5 years

2. **Convert the annual interest rate to a quarterly rate:**
- Since the interest is compounded quarterly, we need to divide the annual interest rate by 4.
- Quarterly Rate (r) = R / 4 = 4% / 4 = 1% per quarter.

3. **Determine the number of compounding periods:**
- Since we are calculating for 6 months and interest is compounded quarterly, there are 2 quarters in 6 months.
- Number of compounding periods (n) = 2.

4. **Use the compound interest formula:**
- The formula for the amount (A) when interest is compounded is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
- Substituting the values:
\[ A = 7500 \left(1 + \frac{1}{100}\right)^2 \]

5. **Calculate the amount:**
- First, calculate \(1 + \frac{1}{100} = 1.01\).
- Then raise it to the power of 2:
\[ (1.01)^2 = 1.0201 \]
- Now multiply by the principal:
\[ A = 7500 \times 1.0201 = 7650.75 \]

6. **Final result:**
- The amount to be paid after 6 months is Rs. 7650.75.

### Summary:
The amount to be paid after 6 months, when Rs. 7500 is borrowed at a compound interest rate of 4% per annum compounded quarterly, is Rs. 7650.75.