A man borrows रु 6,000 at 5 percent C.I. per annum. If he repays रु 1,200 at the end of each year, find the amount of the loan outstanding at the beginning of the third year.

Explanation

To solve the problem step by step, we will calculate the outstanding loan amount at the beginning of the third year after the man has made his repayments at the end of each year.

### Step 1: Calculate the interest for the first year.
The formula for calculating compound interest for the first year is:
\[ \text{Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 6000 \) (the principal amount)
- \( R = 5 \) (the rate of interest)
- \( T = 1 \) (the time period in years)

Substituting the values:
\[ \text{Interest} = \frac{6000 \times 5 \times 1}{100} = \frac{30000}{100} = 300 \]

### Step 2: Calculate the outstanding loan after the first year.
At the end of the first year, the total amount owed will be the principal plus the interest:
\[ \text{Total Amount} = P + \text{Interest} = 6000 + 300 = 6300 \]
Now, the man repays Rs. 1200 at the end of the first year:
\[ \text{Outstanding Loan} = 6300 - 1200 = 5100 \]

### Step 3: Calculate the interest for the second year.
Now, we will calculate the interest on the new principal amount of Rs. 5100 for the second year:
\[ \text{Interest} = \frac{5100 \times 5 \times 1}{100} = \frac{25500}{100} = 255 \]

### Step 4: Calculate the outstanding loan after the second year.
At the end of the second year, the total amount owed will be:
\[ \text{Total Amount} = 5100 + 255 = 5355 \]
After repaying Rs. 1200 at the end of the second year:
\[ \text{Outstanding Loan} = 5355 - 1200 = 4155 \]

### Conclusion
The amount of the loan outstanding at the beginning of the third year is Rs. 4155.

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