Question
Rs. 16000 invested for 2 years in a scheme offering
compound interest (compounded annually) of 15% p.a. gives an interest that is Rs. 25 less than the interest received on investing Rs. Y for a year at simple interest of 25% p.a.. Find the value of ‘Y’.Solution
Interest returned on investing Rs. 16000 = 16000(1 + 15/100)2 – 16000 = 16000(115/100)2 – 16000 = 16000(23/20)2 – 16000 = 16000{232/202)- 1} = 16000{529/400)- 1} = 16000(529 - 400)/400 = Rs. 5160 So, interest returned on investing Rs. Y for 1 year at simple interest of 25% p.a. = 5160 + 25 = Rs. 5185 Or, Y × (25/100) = 5185 Or, Y = 5185 × (100/25) Or, Y = 20740
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