Rs. 7500 is borrowed at Cl at the rate of 4% per annum. What will be the amount to be paid after 1 year, if interest is compounded half-yearly ?

Answer

To solve the problem of finding the amount to be paid after 1 year when Rs. 7500 is borrowed at a compound interest rate of 4% per annum, compounded half-yearly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 7500
- Rate of interest (R) = 4% per annum
- Time (T) = 1 year
- Since the interest is compounded half-yearly, we will divide the time into two periods of 6 months each.

### Step 2: Convert the annual interest rate to half-yearly
Since the interest is compounded half-yearly, we need to divide the annual rate by 2:
- Half-yearly rate (R') = 4% / 2 = 2%

### Step 3: Determine the number of compounding periods
Since the interest is compounded half-yearly for 1 year, the number of compounding periods (n) will be:
- n = 2 (for two half-year periods)

### Step 4: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- A = Amount after time T
- P = Principal amount
- R = Rate of interest per period
- n = Number of compounding periods

### Step 5: Plug in the values
Now we can substitute the values into the formula:
\[ A = 7500 \left(1 + \frac{2}{100}\right)^2 \]
\[ A = 7500 \left(1 + 0.02\right)^2 \]
\[ A = 7500 \left(1.02\right)^2 \]

### Step 6: Calculate \( (1.02)^2 \)
Calculating \( (1.02)^2 \):
\[ (1.02)^2 = 1.0404 \]

### Step 7: Calculate the final amount
Now substitute back to find A:
\[ A = 7500 \times 1.0404 \]
\[ A = 7803 \]

### Conclusion
The amount to be paid after 1 year is Rs. 7803.

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