A money-lender borrows money at 5% per annum and pays the interest at the end of the year. He lends it at 12% per annum compound interest compounded half yearly and receives the interest at the end of 6 months. In this way he gains Rs. 2,944 a year. The amount of money he borrows, is (in rupees)
Let the borrowed amount be x According to the question, x [( 1 + 6/100 )² - 1] –(x × 5 × 1)/100 = 2,944 (since Interest is compounded quarterly ) ⇒ x [ ( 1.06 )² - 1 ] – 0.05x = 2,944 ⇒ 0.1236x - 0.05x = 2,944 ⇒ 0.0736x = 2,944 ⇒ x = 2944/0.0736 = Rs. 40,000
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