Question
Rs. 14000 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. 14000 = 14000(1 + 15/100)2 – 14000 = 14000(115/100)2 – 14000 = 14000(23/20)2 – 14000 = 14000{232/202)- 1} = 14000{529/400)- 1} = 14000(529 - 400)/400 = Rs. 4515 So, interest returned on investing Rs. Y for 1 year at simple interest of 20% p.a. = 4515 + 20 = Rs. 4535 Or, Y × (20/100) = 4535 Or, Y = 4535 × (100/20) Or, Y = 22675
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