A sum of `Rs. 8000` is borrowed at compound Interest at the rate of `7%` per annum. What will be the amount (in Rs.) after 2 years?

Options

A. `1154.4`
B. `13600`
C. `9159.2`
D. `9428.6`

Answer

To find the amount after 2 years when a sum of Rs. 8000 is borrowed at a compound interest rate of 7% per annum, we can use the formula for compound interest:

**Formula:**
\[ A = P \left(1 + \frac{R}{100}\right)^N \]

Where:
- \( A \) = Amount after \( N \) years
- \( P \) = Principal amount (initial sum)
- \( R \) = Rate of interest per annum
- \( N \) = Number of years

### Step 1: Identify the values
- Principal \( P = 8000 \)
- Rate \( R = 7\% \)
- Time \( N = 2 \) years

### Step 2: Substitute the values into the formula
\[ A = 8000 \left(1 + \frac{7}{100}\right)^2 \]

### Step 3: Calculate \( \frac{R}{100} \)
\[ \frac{7}{100} = 0.07 \]

### Step 4: Add 1 to \( \frac{R}{100} \)
\[ 1 + 0.07 = 1.07 \]

### Step 5: Raise the result to the power of \( N \)
\[ (1.07)^2 = 1.1449 \]

### Step 6: Multiply by the principal
\[ A = 8000 \times 1.1449 \]

### Step 7: Calculate the final amount
\[ A = 9159.2 \]

Thus, the amount after 2 years will be **Rs. 9159.2**.

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