What will be the compound interest on a sum of Rs. 25,000 after 3 years at the of 12 p.c.p.a.?

Options

A. Rs. 9000.30
B. Rs. 9720
C. Rs. 9830
D. None of these

Answer

To find the compound interest on a sum of Rs. 25,000 after 3 years at an interest rate of 12% per annum, we can follow these steps:

### Step 1: Identify the formula for compound interest
The formula for calculating the amount (A) after n years with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \( A \) = Amount after n years
- \( P \) = Principal amount (initial sum)
- \( R \) = Rate of interest per annum
- \( n \) = Number of years

### Step 2: Substitute the values into the formula
Given:
- \( P = 25,000 \)
- \( R = 12 \)
- \( n = 3 \)

Substituting these values into the formula:
\[ A = 25000 \left(1 + \frac{12}{100}\right)^3 \]

### Step 3: Simplify the expression inside the parentheses
Calculate \( \frac{12}{100} \):
\[ \frac{12}{100} = 0.12 \]
So,
\[ A = 25000 \left(1 + 0.12\right)^3 \]
\[ A = 25000 \left(1.12\right)^3 \]

### Step 4: Calculate \( (1.12)^3 \)
Now, calculate \( (1.12)^3 \):
\[ (1.12)^3 = 1.12 \times 1.12 \times 1.12 \]
Calculating this gives:
\[ 1.12 \times 1.12 = 1.2544 \]
Then,
\[ 1.2544 \times 1.12 = 1.404928 \]

### Step 5: Calculate the amount (A)
Now substitute back to find A:
\[ A = 25000 \times 1.404928 \]
Calculating this gives:
\[ A = 35123.2 \]

### Step 6: Calculate the compound interest (CI)
To find the compound interest, subtract the principal from the amount:
\[ CI = A - P \]
\[ CI = 35123.2 - 25000 \]
\[ CI = 10123.2 \]

### Final Answer
The compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% per annum is **Rs. 10,123.2**.

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