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Paresh lends Rs. 8 lakhs to a client at an interest rate of 10% per annum, compounded half-yearly. The client repays Rs. 42,000 at the end of the first year, Rs. 66,100 at the end of the second year and closes the loan by paying the outstanding amount at the end of the third year. What is the total interest (in Rs.) earned by Paresh over the three years?1)  2,47,2502)  1,87,2503)  2,75,5004)  2,56,250

Question

Paresh lends Rs. 8 lakhs to a client at an interest rate of 10% per annum, compounded half-yearly. The client repays Rs. 42,000 at the end of the first year, Rs. 66,100 at the end of the second year and closes the loan by paying the outstanding amount at the end of the third year. What is the total interest (in Rs.) earned by Paresh over the three years?1)  2,47,2502)  1,87,2503)  2,75,5004)  2,56,250

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Solution

To solve this problem, we need to calculate the compound interest for each year and then subtract the repayment made by the client.

  1. At the end of the first year: Principal = Rs. 8,00,000 Rate = 10% per annum compounded half-yearly = 5% per half-year Time = 1 year = 2 half-years Compound Interest = P(1 + r/n)^(nt) - P = 8,00,000(1 + 0.05/2)^(2*1) - 8,00,000 = Rs. 81,000 Outstanding amount = Principal + Interest - Repayment = 8,00,000 + 81,000 - 42,000 = Rs. 8,39,000

  2. At the end of the second year: Principal = Rs. 8,39,000 Compound Interest = 8,39,000(1 + 0.05/2)^(2*1) - 8,39,000 = Rs. 85,250 Outstanding amount = 8,39,000 + 85,250 - 66,100 = Rs. 8,58,150

  3. At the end of the third year: Principal = Rs. 8,58,150 Compound Interest = 8,58,150(1 + 0.05/2)^(2*1) - 8,58,150 = Rs. 87,250 Outstanding amount = 8,58,150 + 87,250 = Rs. 9,45,400

The client closes the loan by paying this amount.

The total interest earned by Paresh over the three years is the sum of the compound interest for each year: 81,000 + 85,250 + 87,250 = Rs. 2,53,500

So, the answer is not in the options given. There might be a mistake in the question or the options.

This problem has been solved

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