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      Question

      The difference between compound interest and simple

      interest on a certain sum for 2 years at the same rate of interest is Rs. 144. Also, the simple interest on the same sum for 3 years is Rs. 1800. What will be the amount after 2 years at compound interest?
      A Rs.4000 Correct Answer Incorrect Answer
      B Rs.4425 Correct Answer Incorrect Answer
      C Rs.3844 Correct Answer Incorrect Answer
      D Rs.3305 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let principal = P and rate = r% per annum Simple interest for 3 years = 1800 So, (P × r × 3) / 100 = 1800 Pr/100 = 600 For 2 years, difference between CI and SI = P(r/100)^2 Now, P(r/100)^2 = (Pr/100) × (r/100) = 600 × r/100 = 6r Given, 6r = 144 r = 24% Now, Pr/100 = 600 So, P × 24/100 = 600 P = 2500 Amount after 2 years at CI = 2500 × (1 + 24/100)^2 = 2500 × (1.24)^2 = 2500 × 1.5376 = 3844 Hence, the correct answer is Rs. 3844.

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