On what sum of money will the compound interest for 2 years at 5 per cent per annum amount to Rs 768.75 ?

Answer

To find the sum of money (principal) on which the compound interest for 2 years at 5% per annum amounts to Rs 768.75, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Compound Interest**:
The amount \( A \) after \( n \) years with principal \( P \) and rate \( R \) is given by the formula:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]

2. **Identify the Given Values**:
- Rate \( R = 5\% \)
- Time \( n = 2 \) years
- Compound Interest (CI) = Rs 768.75

3. **Express Amount in Terms of Principal**:
Since the compound interest is the amount minus the principal, we can express the amount \( A \) as:
\[ A = P + \text{CI} \]
Therefore, we can write:
\[ A = P + 768.75 \]

4. **Substitute Values into the Formula**:
Substitute \( R \) and \( n \) into the compound interest formula:
\[ A = P \left(1 + \frac{5}{100}\right)^2 \]
Simplifying the term inside the parentheses:
\[ A = P \left(1 + 0.05\right)^2 = P \left(1.05\right)^2 \]
Now calculate \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Thus, we have:
\[ A = P \times 1.1025 \]

5. **Set Up the Equation**:
Now we can set up the equation using the expression for \( A \):
\[ P + 768.75 = P \times 1.1025 \]

6. **Rearranging the Equation**:
Rearranging gives:
\[ P \times 1.1025 - P = 768.75 \]
Factor out \( P \):
\[ P(1.1025 - 1) = 768.75 \]
Simplifying:
\[ P(0.1025) = 768.75 \]

7. **Solve for Principal \( P \)**:
Now, divide both sides by \( 0.1025 \):
\[ P = \frac{768.75}{0.1025} \]
Calculating the right-hand side:
\[ P = 7500 \]

### Final Answer:
The sum of money (principal) is Rs 7500.

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