S.I. on a sum of money is Rs. 750 for 2 years at 10% per annum. Find the C.I. on that sum for 2 years.

Answer

To solve the problem step by step, we will first find the principal amount using the given simple interest, and then we will calculate the compound interest based on that principal.

### Step 1: Find the Principal Amount

Given:
- Simple Interest (SI) = Rs. 750
- Rate of Interest (R) = 10% per annum
- Time (T) = 2 years

The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Substituting the known values into the formula:
\[ 750 = \frac{P \times 10 \times 2}{100} \]

### Step 2: Simplify the Equation

Rearranging the equation to find P:
\[ 750 = \frac{20P}{100} \]
\[ 750 = \frac{P}{5} \]

### Step 3: Solve for Principal (P)

Multiplying both sides by 5:
\[ P = 750 \times 5 \]
\[ P = 3750 \]

So, the principal amount is Rs. 3750.

### Step 4: Calculate Compound Interest (CI)

The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

Substituting the values:
\[ CI = 3750 \left(1 + \frac{10}{100}\right)^2 - 3750 \]
\[ CI = 3750 \left(1 + 0.1\right)^2 - 3750 \]
\[ CI = 3750 \left(1.1\right)^2 - 3750 \]

### Step 5: Calculate \( (1.1)^2 \)

Calculating \( (1.1)^2 \):
\[ (1.1)^2 = 1.21 \]

### Step 6: Substitute Back into the CI Formula

Now substitute back:
\[ CI = 3750 \times 1.21 - 3750 \]
\[ CI = 4537.5 - 3750 \]

### Step 7: Final Calculation

Calculating the final amount:
\[ CI = 4537.5 - 3750 = 787.5 \]

Thus, the compound interest on the sum for 2 years is Rs. 787.5.

### Summary of Solution
- Principal Amount (P) = Rs. 3750
- Compound Interest (CI) = Rs. 787.5

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