A sum of money is lent out at compound intersect for two years at 20% per annum. Compound intersect being reckoned yearly. If the same sum of money was lent out at compound interest at the same rate percent per annum, compound intersect being reckoned healf-yealry, it would have fetched Rs 482 more by way of interest in two years. Calcualte the sum of money lent out.

Answer

To solve the problem step by step, we will follow the given information and calculate the sum of money lent out based on the compound interest calculated yearly and half-yearly.

### Step 1: Understand the Problem
We need to find the principal amount (P) that was lent out at compound interest for 2 years at a rate of 20% per annum. The interest calculated yearly and half-yearly differs by Rs 482.

### Step 2: Calculate Compound Interest when Reckoned Yearly
1. **Given:**
- Rate (R) = 20% per annum
- Time (T) = 2 years

2. **Formula for Amount (A) when interest is compounded yearly:**
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

3. **Substituting the values:**
\[ A = P \left(1 + \frac{20}{100}\right)^2 = P \left(1 + 0.2\right)^2 = P \left(1.2\right)^2 = P \times 1.44 \]

4. **Thus, the Amount (A) after 2 years is:**
\[ A = 1.44P \]

5. **Calculate Compound Interest (CI) for yearly compounding:**
\[ CI = A - P = 1.44P - P = 0.44P \]

### Step 3: Calculate Compound Interest when Reckoned Half-Yearly
1. **Given:**
- Rate (R) = 20% per annum → Half-yearly rate = 10%
- Time (T) = 2 years → Number of half-year periods = 4

2. **Formula for Amount (A) when interest is compounded half-yearly:**
\[ A = P \left(1 + \frac{R/2}{100}\right)^{2T} \]

3. **Substituting the values:**
\[ A = P \left(1 + \frac{10}{100}\right)^4 = P \left(1 + 0.1\right)^4 = P \left(1.1\right)^4 \]

4. **Calculating \( (1.1)^4 \):**
\[ (1.1)^4 = 1.4641 \]
So,
\[ A = 1.4641P \]

5. **Calculate Compound Interest (CI) for half-yearly compounding:**
\[ CI = A - P = 1.4641P - P = 0.4641P \]

### Step 4: Set Up the Equation Based on the Given Information
1. **According to the problem, the difference in interest is Rs 482:**
\[ 0.4641P - 0.44P = 482 \]

2. **Simplifying the equation:**
\[ 0.0241P = 482 \]

### Step 5: Solve for Principal (P)
1. **To find P:**
\[ P = \frac{482}{0.0241} \approx 20000 \]

### Conclusion
The sum of money lent out is Rs 20,000.

---