Question
A certain sum is invested at a compound interest rate,
compounded annually, which grows to Rs. 12,240 after 2 years and to Rs. 17,625.6 after 4 years. If 80% of this sum is then invested at a simple interest rate of 7% per annum for 10 years, calculate the simple interest earned on this investment.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 invested at simple interest = 8500 X 0.8 = Rs. 6,800 So, simple interest earned = 6800 X 7 X 10 ÷ 100 = Rs. 4760
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