Find the simple interest and compound interest on Rs 10000 for 2 years at the rate of 10%?

Options

A. ₹ 2100, ₹ 2500
B. ₹ 2000, ₹2100
C. ₹ 2100, ₹2000
D. ₹ 2000, ₹ 2500

Answer

To find the simple interest and compound interest on Rs 10,000 for 2 years at the rate of 10%, 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 10,000)
- \( R \) = Rate of interest (10%)
- \( T \) = Time (2 years)

Substituting the values into the formula:

\[ SI = \frac{10000 \times 10 \times 2}{100} \]

Calculating this gives:

\[ SI = \frac{100000}{100} = 1000 \]

So, the Simple Interest for 2 years is Rs 2000.

### 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 10,000)
- \( R \) = Rate of interest (10%)
- \( T \) = Time (2 years)

Substituting the values into the formula:

\[ A = 10000 \left(1 + \frac{10}{100}\right)^2 \]

Calculating this gives:

\[ A = 10000 \left(1 + 0.1\right)^2 = 10000 \left(1.1\right)^2 \]

Calculating \( (1.1)^2 \):

\[ (1.1)^2 = 1.21 \]

Now substituting back:

\[ A = 10000 \times 1.21 = 12100 \]

Now, to find the Compound Interest:

\[ CI = A - P = 12100 - 10000 = 2100 \]

### Final Results

- Simple Interest (SI) = Rs 2000
- Compound Interest (CI) = Rs 2100