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?

Options

A. ₹ 150
B. ₹ 180
C. ₹ 210
D. ₹ 316

Answer

To find the difference between compound interest (CI) and simple interest (SI) on an amount of Rs. 18,000 over 2 years at a rate of 10% per year, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount = Rs. 18,000
- \(R\) = Rate of interest = 10%
- \(T\) = Time in years = 2

Substituting the values:
\[ SI = \frac{18000 \times 10 \times 2}{100} \]
\[ SI = \frac{180000}{100} = 1800 \]

### Step 2: Calculate Compound Interest (CI)
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal amount = Rs. 18,000
- \(R\) = Rate of interest = 10%
- \(T\) = Time in years = 2

Substituting the values:
\[ A = 18000 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 18000 \left(1 + 0.1\right)^2 = 18000 \times (1.1)^2 \]
\[ A = 18000 \times 1.21 = 21780 \]

Now, to find the compound interest:
\[ CI = A - P = 21780 - 18000 = 3780 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = CI - SI = 3780 - 1800 = 1980 \]

### Final Answer
The difference between compound interest and simple interest is Rs. 1980.

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