Question
sum invested at a certain rate of compound interest,
compounded annually amounts to Rs.12,240 after 2 years and amounts to Rs. 17,625.6 after 4 years. If 60% of the sum is invested in the simple interest of 7p.a 10 years, then find the simple interest earned.Solution
Let the sum invested = Rs. 'K' Let the rate of interest = 'y'% p.a. Then, according to the question K X {1 + (y/100)} ² = 12,240 ....... (I) And K X {1 + (y/100)} ⁴ = 17625.6 ........ (II) On dividing equation (I) from equation (II), we have. {1 + (y/100)} ² = 1.44 Or, 1 + (y/100) = 1.2 Or (y/100) = 0.2 So, y = 20 Therefore, sum invested = 12240 ÷ {(100 +20)/100} ² = 12240 ÷ 1.44 = Rs. 8,500 so, sum invest at simple interest= 8500×60/100=5100 so simple interest earned =5100×7×10/100=3570rs
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