Question
Raj invests a certain amount,
which grows to Rs. 7,200 at the end of 2 years and further increases to Rs. 8,640 at the end of 3 years, at a specific annual compound interest rate (compounded yearly). Determine the initial amount Raj invested.Solution
ATQ, Let the sum invested be Rs. ‘P’ and rate of interest be ‘R%’ p.a. ATQ; P × {1 + (R/100)}2 = 7200 ……… (i) P × {1 + (R/100)}3 = 8640 ………. (ii) On, dividing equation (ii) by equation (i), we have; {1 + (R/100)} = 1.2 Or, (R/100) = 0.2 Or, R = 20 Therefore, rate of interest is 20% p.a. On putting R = 20 in equation (i), we have; P × {1 + (20/100)}2 = 7200 Or, P = 7200 ÷ 1.44 So, P = 5000 Therefore, the sum invested was Rs.5,000
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