What is the difference between the compound interest and simple interest accrued on an amount of ₹12,000 at the end of three years at the rate of 12% ?

Options

A. ₹539.136
B. ₹602.242
C. ₹495.248
D. ₹488.322

Explanation

To find the difference between the compound interest (CI) and simple interest (SI) accrued on an amount of ₹12,000 at the end of three years at the rate of 12%, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)

The formula for calculating Simple Interest is:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (₹12,000)
- \( R \) = Rate of interest (12%)
- \( T \) = Time period (3 years)

Substituting the values:

\[ SI = \frac{12000 \times 12 \times 3}{100} \]

Calculating:

\[ SI = \frac{12000 \times 36}{100} = \frac{432000}{100} = 4320 \]

So, the Simple Interest accrued is ₹4,320.

### Step 2: Calculate Compound Interest (CI)

The formula for calculating Compound Interest is:

\[ CI = A - P \]

Where \( A \) is the amount after \( n \) years, calculated using the formula:

\[ A = P \left(1 + \frac{R}{100}\right)^n \]

Substituting the values:

\[ A = 12000 \left(1 + \frac{12}{100}\right)^3 \]

Calculating \( 1 + \frac{12}{100} = 1.12 \):

\[ A = 12000 \times (1.12)^3 \]

Calculating \( (1.12)^3 \):

\[ (1.12)^3 = 1.404928 \]

Now substituting back to find \( A \):

\[ A = 12000 \times 1.404928 \approx 16859.136 \]

Now, we can find the Compound Interest:

\[ CI = A - P = 16859.136 - 12000 \approx 4859.136 \]

So, the Compound Interest accrued is approximately ₹4,859.136.

### Step 3: Calculate the Difference between CI and SI

Now, we find the difference:

\[ \text{Difference} = CI - SI = 4859.136 - 4320 \]

Calculating the difference:

\[ \text{Difference} = 539.136 \]

### Conclusion

The difference between the compound interest and simple interest accrued on an amount of ₹12,000 at the end of three years at the rate of 12% is approximately ₹539.136.

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