If SI on a certain sum of money at 4% per annum for 2 years be Rs. 125, what would be the interest if it was to be compounded annually at the same rate and for the same time period?

Options

A. Rs. 127.50
B. Rs. 125.50
C. Rs. 135.50
D. Rs. 138

Answer

To solve the problem step by step, we need to find the compound interest (CI) based on the information provided about simple interest (SI). Here's how we can do it:

### Step 1: Understand the given information
We know:
- Simple Interest (SI) = Rs. 125
- Rate of Interest (R) = 4% per annum
- Time (T) = 2 years

### Step 2: Use the formula for Simple Interest to find the Principal (P)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the known values:
\[ 125 = \frac{P \times 4 \times 2}{100} \]
This simplifies to:
\[ 125 = \frac{8P}{100} \]
Multiplying both sides by 100:
\[ 12500 = 8P \]
Now, divide both sides by 8 to find P:
\[ P = \frac{12500}{8} = 1562.5 \]

### Step 3: Calculate 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. We can substitute the values we have:
\[ A = 1562.5 \left(1 + \frac{4}{100}\right)^2 \]
This simplifies to:
\[ A = 1562.5 \left(1 + 0.04\right)^2 = 1562.5 \left(1.04\right)^2 \]
Calculating \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]
Now substituting back:
\[ A = 1562.5 \times 1.0816 = 1690.00 \]

### Step 4: Find the Compound Interest (CI)
Now, we can find the Compound Interest using:
\[ CI = A - P \]
Substituting the values we found:
\[ CI = 1690.00 - 1562.5 = 127.5 \]

### Final Answer
The compound interest for the same sum of money at 4% per annum for 2 years is **Rs. 127.5**.

---