Find the simple interest and compound interest on Rs 20000 for 3 years at the rate of 5%?

Options

A. ₹ 3100, ₹ 3152.5
B. ₹ 3100, ₹ 3000
C. ₹ 3100, ₹ 3152.5
D. ₹ 3000, ₹ 3152.5

Answer

To find the Simple Interest (SI) and Compound Interest (CI) on Rs 20,000 for 3 years at the rate of 5%, 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 20,000)
- \( R \) = Rate of interest (5%)
- \( T \) = Time in years (3 years)

Substituting the values:

\[ SI = \frac{20000 \times 5 \times 3}{100} \]

Calculating it step by step:

1. Calculate \( 20000 \times 5 = 100000 \)
2. Then, \( 100000 \times 3 = 300000 \)
3. Finally, divide by 100: \( \frac{300000}{100} = 3000 \)

So, the Simple Interest is:

\[ SI = Rs 3000 \]

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

The formula for Compound Interest is:

\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

Substituting the values:

\[ CI = 20000 \left(1 + \frac{5}{100}\right)^3 - 20000 \]

Calculating it step by step:

1. Calculate \( 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \)
2. Calculate \( (1.05)^3 \):
- \( 1.05 \times 1.05 = 1.1025 \)
- \( 1.1025 \times 1.05 = 1.157625 \)
3. Now, multiply by the principal:
- \( 20000 \times 1.157625 = 23152.5 \)
4. Finally, subtract the principal:
- \( 23152.5 - 20000 = 3152.5 \)

So, the Compound Interest is:

\[ CI = Rs 3152.5 \]

### Summary of Results
- Simple Interest (SI) = Rs 3000
- Compound Interest (CI) = Rs 3152.5

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