Mr. Ibrahim borrowed Rs. 7500 at 5% per annum compound interest. The compound interest compouned annally for 2 years is.

Options

A. 768.75
B. 8268.75
C. 8286.75
D. 786.75

Answer

To find the compound interest for Mr. Ibrahim who borrowed Rs. 7500 at an interest rate of 5% per annum for 2 years, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 7500
- Rate of interest (r) = 5% per annum
- Time (T) = 2 years

### Step 2: Use the compound interest formula
The formula for the amount (A) after T years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ A = 7500 \left(1 + \frac{5}{100}\right)^2 \]

### Step 4: Simplify the expression
Calculating the term inside the parentheses:
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]
Now substituting this back into the equation:
\[ A = 7500 \times (1.05)^2 \]

### Step 5: Calculate \( (1.05)^2 \)
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Now substituting this value into the equation for A:
\[ A = 7500 \times 1.1025 \]

### Step 6: Calculate the total amount
Calculating the amount:
\[ A = 7500 \times 1.1025 = 8268.75 \]

### Step 7: Calculate the compound interest
The compound interest (CI) is given by:
\[ CI = A - P \]
Substituting the values we have:
\[ CI = 8268.75 - 7500 \]

### Step 8: Final calculation
Calculating the compound interest:
\[ CI = 768.75 \]

### Conclusion
The compound interest for Mr. Ibrahim after 2 years is **Rs. 768.75**.

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