Question
Rs. 2000 invested for 2 years in a scheme offering
compound interest (compounded annually) of 15% p.a. gives an interest that is Rs. 20 less than the interest received on investing Rs. Y for a year at simple interest of 20% p.a.. Find the value of ‘Y’.Solution
Interest returned on investing Rs. 2000 = 2000(1 + 15/100)2 – 2000 = 2000(115/100)2 – 2000 = 2000(23/20)2 – 2000 = 2000{232/202)- 1} = 2000{529/400)- 1} = 2000(529 - 400)/400 = Rs. 645 So, interest returned on investing Rs. Y for 1 year at simple interest of 20% p.a. = 645 + 20 = Rs. 665 Or, Y × (20/100) = 665 Or, Y = 665 × (100/20) Or, Y = 3325
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