Mr. Mike borrowed Rs. 8500 at `4%` per annum compound interest . The compound interest compounded annually for 2 years is

Options

A. Rs. 9139.6
B. Rs. 639.6
C. Rs. 9193.6
D. Rs. 693.6

Answer

To find the compound interest for Mr. Mike's loan, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 8500
- Rate of interest (r) = 4% per annum
- Time (t) = 2 years

### Step 2: Convert the rate of interest into decimal
To use the formula, we need to convert the percentage into a decimal:
\[ r = \frac{4}{100} = 0.04 \]

### Step 3: Use the compound interest formula
The formula for the amount (A) after t years with compound interest is:
\[ A = P \left(1 + r\right)^t \]

### Step 4: Substitute the values into the formula
Now, substituting the values into the formula:
\[ A = 8500 \left(1 + 0.04\right)^2 \]
\[ A = 8500 \left(1.04\right)^2 \]

### Step 5: Calculate \((1.04)^2\)
Calculating \((1.04)^2\):
\[ (1.04)^2 = 1.0816 \]

### Step 6: Calculate the total amount (A)
Now, substituting back into the equation:
\[ A = 8500 \times 1.0816 \]
\[ A = 9193.6 \]

### Step 7: Calculate the compound interest (CI)
The compound interest is given by:
\[ CI = A - P \]
\[ CI = 9193.6 - 8500 \]
\[ CI = 693.6 \]

### Final Answer
The compound interest compounded annually for 2 years is Rs. 693.6.

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