The difference between simple interest and the compound interest compounded annually at the rate of 12% per annum on ₹ 5,000 for two years will be :

Question

Accepted Answer

To determine the difference between the simple interest and the compound interest compounded annually at the rate of 12% per annum on ₹ 5,000 for two years, we need to calculate both types of interest and then find their difference.

1. **Simple Interest (SI):**
   - Formula: $ \text{SI} = \frac{P \times R \times T}{100} $
   - Where $ P = 5000 $, $ R = 12\% $, $ T = 2 $ years.
   - Calculation: 
     $$
     \text{SI} = \frac{5000 \times 12 \times 2}{100} = 1200
     $$

2. **Compound Interest (CI):**
   - Formula: $ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P $
   - Calculation:
     $$
     \text{CI} = 5000 \left(1 + \frac{12}{100}\right)^2 - 5000
     $$
     $$
     = 5000 \left(1.12\right)^2 - 5000
     $$
     $$
     = 5000 \times 1.2544 - 5000
     $$
     $$
     = 6272 - 5000 = 1272
     $$

3. **Difference between CI and SI:**
   - Difference = $ \text{CI} - \text{SI} = 1272 - 1200 = 72 $

Therefore, the difference between the simple interest and the compound interest is ₹ 72, which corresponds to Option 1.

**Explanation for Other Options:**

- **Option 2 (₹ 84):** This option is incorrect because the calculated difference between the compound interest and simple interest is ₹ 72, not ₹ 84. The calculations clearly show that the difference is ₹ 72.

- **Option 3 (₹ 96):** This option is incorrect for the same reason as above. The actual difference is ₹ 72, and there is no calculation or scenario in this context that would result in a difference of ₹ 96.

- **Option 4 (₹ 36):** This option is incorrect because the difference calculated is ₹ 72. A difference of ₹ 36 does not match the calculations derived from the given interest rates and principal amount.

In conclusion, the correct answer is Option 1 (₹ 72), as it accurately reflects the difference between the simple interest and compound interest for the given conditions.