The compound Interest on a cer tain sum for 2 years at the rate of `5% `per annum compounded annually is `Rs. 205`. What is the simple interest in the same case?

Options

A. A) `Rs. 210`
B. B) `Rs. 220`
C. C) `Rs. 250 `
D. D) `Rs. 200 `

Answer

To find the simple interest when the compound interest for 2 years at a rate of 5% per annum is given as Rs. 205, we can follow these steps:

### Step 1: Understand the relationship between Compound Interest (CI) and Simple Interest (SI)
The formula for Compound Interest for 2 years can be derived as follows:
- The total amount (A) after 2 years can be calculated using the formula:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where \( P \) is the principal, \( r \) is the rate of interest, and \( n \) is the number of years.

For 2 years at 5%:
\[ A = P \left(1 + \frac{5}{100}\right)^2 = P \left(1.05\right)^2 = P \times 1.1025 \]

The Compound Interest (CI) for 2 years is given by:
\[ CI = A - P = P \times 1.1025 - P = P \times 0.1025 \]

### Step 2: Set up the equation using the given CI
We know that the Compound Interest for 2 years is Rs. 205:
\[ P \times 0.1025 = 205 \]

### Step 3: Solve for the principal (P)
To find \( P \):
\[ P = \frac{205}{0.1025} \]

Calculating this:
\[ P = \frac{205 \times 10000}{1025} = \frac{2050000}{1025} = 2000 \]

### Step 4: Calculate the Simple Interest (SI)
The formula for Simple Interest for 2 years is:
\[ SI = \frac{P \times r \times n}{100} \]
Substituting the values:
\[ SI = \frac{2000 \times 5 \times 2}{100} = \frac{20000}{100} = 200 \]

### Final Answer
The Simple Interest in this case is **Rs. 200**.

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