The difference between the CI and SI on a certain sum of money at 5% per annum for 2 years is Rs. 1.50, Find the sum

Answer

To find the sum of money (principal) based on the given information about the difference between Compound Interest (CI) and Simple Interest (SI), we can follow these steps:

### Step 1: Understand the formula for the difference between CI and SI
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years can be calculated using the formula:
\[ \text{Difference} = \frac{P \times R^2}{100^2} \]
where:
- \( P \) is the principal amount (the sum of money we want to find),
- \( R \) is the rate of interest (5% in this case),
- The difference is given as Rs. 1.50.

### Step 2: Substitute the known values into the formula
Given that the rate \( R = 5\% \) and the difference is Rs. 1.50, we can substitute these values into the formula:
\[ 1.50 = \frac{P \times (5)^2}{100^2} \]

### Step 3: Simplify the equation
Calculating \( (5)^2 \) and \( (100)^2 \):
\[ (5)^2 = 25 \quad \text{and} \quad (100)^2 = 10000 \]
Now, substitute these values back into the equation:
\[ 1.50 = \frac{P \times 25}{10000} \]

### Step 4: Rearrange the equation to solve for \( P \)
Multiply both sides by 10000 to eliminate the fraction:
\[ 1.50 \times 10000 = P \times 25 \]
\[ 15000 = P \times 25 \]
Now, divide both sides by 25 to isolate \( P \):
\[ P = \frac{15000}{25} \]

### Step 5: Calculate the value of \( P \)
Now, perform the division:
\[ P = 600 \]

### Conclusion
The sum of money (principal) is Rs. 600.

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