Question
'X' invested Rs. (x + 3000) at compound interest of 20%
p.a. compounded annually. 1 year later, he invested Rs. '2x' at simple interest of 15% p.a. If 3 years after making the 1st investment, total interest earned from both investments is Rs. 8,824, then determine the amount invested by 'X' at compound interest.ÂSolution
ATQ, Compound interest = Sum X {1 + (rate of interest/100) }time period - Sum So, compound interest earned = (x + 3000) X [{1 + (20/100) }3 - 1] = (x + 3000) X (1.728 - 1) = (x + 3000) X 0.728 = Rs. (0.728x + 2184) And simple interest = [Sum X rate of interest X time period in years] Ă· 100 So simple interest earned = [2x X 15 X 2] Ă· 100 = Rs. '0.6x' ATQ; 0.728x + 2184 + 0.6x = 8824 Or, 1.328x = 6640 So, 'x' = 5000 So, sum invested by 'X' at compound interest = 5000 + 3000 = Rs.8,000
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