Anil borrows Rs. 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs. 10,320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to

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1. **Calculate Outstanding Amount After First Year:**  
   The principal borrowed is Rs. 2,00,000, and the interest rate is 8% per annum compounded half-yearly (4% per half-year). After one year (two compounding periods):  
   $$
   	ext{Amount after 1 year} = 2,00,000 	imes (1.04)^2 = 2,16,320.
   $$  
   Anil repays Rs. 10,320 at the end of the first year:  
   $$
   	ext{Outstanding principal} = 2,16,320 - 10,320 = 2,06,000.
   $$

2. **Calculate Amount After Three Years (Remaining Loan):**  
   The outstanding principal of Rs. 2,06,000 accrues interest for two more years (four compounding periods):  
   $$
   	ext{Amount after 3 years} = 2,06,000 	imes (1.04)^4 = Rs. 2,40,990.8634 \approx Rs. 2,40,991.
   $$

3. **Total Amount Paid by Anil:**  
   - First payment: Rs. 10,320  
   - Final payment: Rs. 2,40,991  
   $$
   	ext{Total amount paid} = 10,320 + 2,40,991 = Rs. 2,51,311.
   $$

4. **Total Interest Paid:**  
   The total interest is calculated as:  
   $$
   	ext{Interest} = 	ext{Total amount paid} - 	ext{Principal borrowed} = 2,51,311 - 2,00,000 = Rs. 51,311.
   $$

Thus, the total interest paid over three years is **Rs. 51,311**.

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