What is the difference between the compound interest and simple interest accrued on an amount of ₹16,200 at the end of three years at the rate of 25% ? ( Rounded off to two digits after decimal.)

Options

A. `3213.44`
B. `3302.42`
C. `3495.28`
D. `3290.63`

Explanation

To find the difference between the compound interest (CI) and simple interest (SI) accrued on an amount of ₹16,200 at the end of three years at the rate of 25%, we can follow these steps:

### Step 1: Calculate the Compound Interest (CI)
The formula for compound interest is:
\[ CI = P \left(1 + \frac{r}{100}\right)^n - P \]
Where:
- \( P \) = Principal amount (₹16,200)
- \( r \) = Rate of interest (25%)
- \( n \) = Time in years (3)

Substituting the values:
\[ CI = 16200 \left(1 + \frac{25}{100}\right)^3 - 16200 \]
\[ = 16200 \left(1 + 0.25\right)^3 - 16200 \]
\[ = 16200 \left(1.25\right)^3 - 16200 \]

Calculating \( (1.25)^3 \):
\[ (1.25)^3 = 1.953125 \]
So,
\[ CI = 16200 \times 1.953125 - 16200 \]
\[ = 31656.25 - 16200 \]
\[ = 15456.25 \]

### Step 2: Calculate the Simple Interest (SI)
The formula for simple interest is:
\[ SI = \frac{P \times r \times n}{100} \]
Substituting the values:
\[ SI = \frac{16200 \times 25 \times 3}{100} \]
\[ = \frac{16200 \times 75}{100} \]
\[ = 16200 \times 0.75 \]
\[ = 12150 \]

### Step 3: Find the Difference Between CI and SI
Now, we find the difference:
\[ \text{Difference} = CI - SI \]
\[ = 15456.25 - 12150 \]
\[ = 3306.25 \]

### Step 4: Round Off the Result
Rounding off to two decimal places:
\[ \text{Difference} \approx 3306.25 \]

### Final Answer
The difference between the compound interest and simple interest accrued on an amount of ₹16,200 at the end of three years at the rate of 25% is approximately **₹3306.25**.

---