On a certain sum of money, the simple interest for 2 years is `Rs. 350` at the rate of `4%` per annum. It was invested at compound interest at the same rate for the same duration as before, how much more Interest would be earned?

Options

A. `Rs. 3.50`
B. `Rs. 7 `
C. `Rs. 14 `
D. `Rs. 35`

Answer

To solve the problem, we need to calculate the difference between the compound interest (CI) and simple interest (SI) earned on the same principal amount over the same time period at the same interest rate.

### Step-by-Step Solution:

1. **Calculate the Principal Amount (P)**:
We know the formula for Simple Interest (SI):
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI = 350 \) (given)
- \( R = 4\% \) (rate of interest)
- \( T = 2 \) years (time)

Rearranging the formula to find \( P \):
\[ P = \frac{SI \times 100}{R \times T} \]
Substituting the values:
\[ P = \frac{350 \times 100}{4 \times 2} = \frac{35000}{8} = 4375 \]

2. **Calculate the Compound Interest (CI)**:
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) is the total amount after time \( T \).
- \( P = 4375 \)
- \( R = 4\% \)
- \( T = 2 \)

Substituting the values:
\[ A = 4375 \left(1 + \frac{4}{100}\right)^2 = 4375 \left(1 + 0.04\right)^2 = 4375 \times (1.04)^2 \]
Calculating \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]
Now calculating \( A \):
\[ A = 4375 \times 1.0816 = 4726 \]

The Compound Interest (CI) can be calculated as:
\[ CI = A - P = 4726 - 4375 = 351 \]

3. **Calculate the Difference Between CI and SI**:
Now we find the difference between the Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI = 351 - 350 = 1 \]

4. **Final Answer**:
The amount of more interest earned through Compound Interest compared to Simple Interest is:
\[ \text{More Interest} = 1 \text{ Rs} \]