Find the compound interest on Rs `25000` for `3` years at `10%` per annum, compounded annually.

Options

A. `8255`
B. `8275`
C. `8285`
D. `8265`

Answer

To find the compound interest on Rs 25,000 for 3 years at a rate of 10% per annum, compounded annually, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 25,000
- Rate (r) = 10% per annum
- Time (n) = 3 years

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

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ A = 25000 \left(1 + \frac{10}{100}\right)^3 \]

### Step 4: Simplify the expression inside the parentheses
Calculate \( 1 + \frac{10}{100} \):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]

### Step 5: Raise the result to the power of n
Now raise \( 1.1 \) to the power of 3:
\[ A = 25000 \times (1.1)^3 \]

Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.331 \]

### Step 6: Calculate the total amount (A)
Now substitute back into the equation:
\[ A = 25000 \times 1.331 \]
\[ A = 33275 \]

### Step 7: Calculate the compound interest (CI)
Now, to find the compound interest, we subtract the principal from the total amount:
\[ CI = A - P \]
\[ CI = 33275 - 25000 \]
\[ CI = 8275 \]

### Final Answer
The compound interest on Rs 25,000 for 3 years at 10% per annum is Rs 8,275.

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