Find compound interest on Rs 62500 for 2 years 6 months at 12% per annum compounded annally.

Answer

To find the compound interest on Rs 62,500 for 2 years and 6 months at an interest rate of 12% per annum compounded annually, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 62,500
- Rate of interest (R) = 12% per annum
- Time (T) = 2 years 6 months = 2.5 years (or 2 + 6/12 = 2.5)

**Hint:** Always convert the time into years when dealing with compound interest.

### Step 2: 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
- \( R \) = Rate of interest
- \( n \) = Number of years

**Hint:** The amount \( A \) is what you will have after the interest is applied.

### Step 3: Substitute the values into the formula
Here, \( n = 2.5 \) years, so we substitute the values:
\[ A = 62500 \left(1 + \frac{12}{100}\right)^{2.5} \]

**Hint:** Make sure to convert the percentage into a decimal when performing calculations.

### Step 4: Calculate \( 1 + \frac{R}{100} \)
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

**Hint:** This step simplifies the calculation by converting the percentage to a decimal.

### Step 5: Calculate \( (1.12)^{2.5} \)
To calculate \( (1.12)^{2.5} \), we can break it down:
\[ (1.12)^{2.5} = (1.12^2)^{1.25} \]
First, calculate \( 1.12^2 \):
\[ 1.12^2 = 1.2544 \]
Then, raise it to the power of \( 1.25 \):
\[ (1.2544)^{1.25} \approx 1.309 \]

**Hint:** Use a calculator for powers to ensure accuracy.

### Step 6: Calculate the amount \( A \)
Now substitute back into the formula:
\[ A = 62500 \times 1.309 \approx 81812.50 \]

**Hint:** Ensure you multiply correctly to find the total amount.

### Step 7: Calculate the compound interest (CI)
Now, we find the compound interest using:
\[ CI = A - P \]
\[ CI = 81812.50 - 62500 = 19312.50 \]

**Hint:** The compound interest is the extra amount earned over the principal.

### Final Answer
The compound interest on Rs 62,500 for 2 years and 6 months at 12% per annum compounded annually is approximately Rs 19,312.50.

---