Question
Rs. 15000 invested for 2 years in a scheme offering
compound interest (compounded annually) of 15% p.a. gives an interest that is Rs. 50 less than the interest received on investing Rs. Y for a year at simple interest of 50% p.a.. Find the value of ‘Y’.Solution
Interest returned on investing Rs. 15000 = 15000(1 + 15/100)2 – 15000 = 15000(115/100)2 – 15000 = 15000(23/20)2 – 15000 = 15000{232/202)- 1} = 15000{529/400)- 1} = 15000(529 - 400)/400 = Rs. 4837.5 So, interest returned on investing Rs. Y for 1 year at simple interest of 50% p.a. = 4837.5 + 50 = Rs. 4887.5 Or, Y × (50/100) = 4887.5 Or, Y = 4887.5 × (100/50) Or, Y = 9775
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