What is the difference between Compound interest and Simple interest on the amount of Rs. 18,000 in 2 years with the rate of 10% per year ?

Question

Accepted Answer

To determine the difference between compound interest and simple interest on an amount of Rs. 18,000 over 2 years at a rate of 10% per annum, we need to calculate both types of interest and then find their difference.

### Simple Interest (SI):
Simple Interest is calculated using the formula:
$$ \text{SI} = \frac{P \times R \times T}{100} $$
where $ P $ is the principal amount, $ R $ is the rate of interest per annum, and $ T $ is the time in years.

For this problem:
- $ P = 18,000 $
- $ R = 10\% $
- $ T = 2 $ years

$$ \text{SI} = \frac{18,000 \times 10 \times 2}{100} = 3,600 $$

### Compound Interest (CI):
Compound Interest is calculated using the formula:
$$ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P $$

For this problem:
$$ \text{CI} = 18,000 \left(1 + \frac{10}{100}\right)^2 - 18,000 $$
$$ \text{CI} = 18,000 \left(1.1\right)^2 - 18,000 $$
$$ \text{CI} = 18,000 \times 1.21 - 18,000 $$
$$ \text{CI} = 21,780 - 18,000 = 3,780 $$

### Difference between CI and SI:
$$ \text{Difference} = \text{CI} - \text{SI} = 3,780 - 3,600 = 180 $$

Thus, the difference between the compound interest and simple interest is Rs. 180, which corresponds to **Option 2**.

### Explanation of Other Options:
1. **Option 1 (Rs. 150):** This option is incorrect because the calculated difference is Rs. 180, not Rs. 150.
2. **Option 3 (Rs. 210):** This option is incorrect because the calculated difference is Rs. 180, not Rs. 210.
3. **Option 4 (Rs. 316):** This option is incorrect because the calculated difference is Rs. 180, not Rs. 316.

Therefore, based on the calculations and logical reasoning, **Option 2 (Rs. 180)** is the correct answer.