Find the sum of money which when invested for `4` years at `5%` per annum yields an amount of `₹540`.

Answer

To find the sum of money (Principal) that yields an amount of ₹540 when invested for 4 years at an interest rate of 5% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Amount (A) = ₹540
- Rate (R) = 5% per annum
- Time (T) = 4 years

2. **Recall the formula for the amount**:
The formula for the amount (A) in terms of Principal (P) and Simple Interest (SI) is:
\[ A = P + SI \]

3. **Recall the formula for Simple Interest (SI)**:
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the given values into this formula:
\[ SI = \frac{P \times 5 \times 4}{100} = \frac{20P}{100} = \frac{1}{5}P \]

4. **Substitute SI into the amount formula**:
Now, substitute the value of SI into the amount formula:
\[ A = P + SI \]
This becomes:
\[ 540 = P + \frac{1}{5}P \]

5. **Combine the terms**:
Combine the terms on the right side:
\[ 540 = P + \frac{1}{5}P = \frac{5P}{5} + \frac{1P}{5} = \frac{6P}{5} \]

6. **Solve for P**:
To isolate P, multiply both sides by 5:
\[ 540 \times 5 = 6P \]
\[ 2700 = 6P \]
Now, divide both sides by 6:
\[ P = \frac{2700}{6} = 450 \]

7. **Conclusion**:
The sum of money (Principal) that yields an amount of ₹540 when invested for 4 years at 5% per annum is:
\[ P = ₹450 \]