What will be the compound interest on Rs. 15625 for 3 years at 8% per annum, if the interest is compounded annually ?

Options

A. Rs 4805
B. Rs. 4508
C. Rs. 4580
D. Rs. 4058

Explanation

To find the compound interest on Rs. 15625 for 3 years at an interest rate of 8% per annum, compounded annually, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 15625
- Rate of interest (R) = 8% per annum
- Time (T) = 3 years

### Step 2: Use the formula for compound interest
The formula for calculating the amount (A) after time T 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:
\[ A = 15625 \left(1 + \frac{8}{100}\right)^3 \]

### Step 4: Simplify the expression
First, calculate \( \frac{8}{100} \):
\[ \frac{8}{100} = 0.08 \]
So,
\[ A = 15625 \left(1 + 0.08\right)^3 \]
\[ A = 15625 \left(1.08\right)^3 \]

### Step 5: Calculate \( (1.08)^3 \)
Now, calculate \( (1.08)^3 \):
\[ (1.08)^3 = 1.08 \times 1.08 \times 1.08 = 1.259712 \]

### Step 6: Calculate the total amount
Now substitute this back into the equation for A:
\[ A = 15625 \times 1.259712 \]
Calculating this gives:
\[ A \approx 19683.00 \]

### Step 7: Calculate the compound interest
Now, to find the compound interest (CI), we use the formula:
\[ CI = A - P \]
Substituting the values we have:
\[ CI = 19683 - 15625 \]
\[ CI = 4058 \]

### Final Answer
The compound interest on Rs. 15625 for 3 years at 8% per annum, compounded annually, is **Rs. 4058**.

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