If the simple interest for 2 years is Rs. 500 at 10% rate of interest. Find the compound interest for the same time.

Options

A. Rs 525
B. Rs 500
C. Rs 200
D. Rs 210

Answer

To solve the problem of finding the compound interest for the same time period and rate given that the simple interest for 2 years is Rs. 500 at a 10% rate of interest, we can follow these steps:

### Step 1: Understand the given information
- Simple Interest (SI) = Rs. 500
- Rate of Interest (R) = 10%
- Time (T) = 2 years

### Step 2: Use the Simple Interest formula to find the Principal (P)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 500 = \frac{P \times 10 \times 2}{100} \]

### Step 3: Rearranging the equation to solve for Principal (P)
Cross-multiplying gives:
\[ 500 \times 100 = P \times 10 \times 2 \]
\[ 50000 = 20P \]
Now, divide both sides by 20:
\[ P = \frac{50000}{20} = 2500 \]

### Step 4: Use the Principal to find the Compound Interest (CI)
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where A is the amount after time T. Substituting the values we have:
\[ A = 2500 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 2500 \left(1 + 0.1\right)^2 = 2500 \left(1.1\right)^2 \]

### Step 5: Calculate \( (1.1)^2 \)
Calculating \( (1.1)^2 \):
\[ (1.1)^2 = 1.21 \]
So,
\[ A = 2500 \times 1.21 = 3025 \]

### Step 6: Calculate the Compound Interest (CI)
Now, we find the Compound Interest by subtracting the Principal from the Amount:
\[ CI = A - P = 3025 - 2500 = 525 \]

### Final Answer
The Compound Interest for the same time period is Rs. 525.

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