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      Question

      The extra interest earned from compound interest over

      simple interest on a sum of money after 2 years (with interest compounded semi-annually) is Rs. 972. If the yearly interest rate is 12%, determine the principal.
      A Rs.52,000 Correct Answer Incorrect Answer
      B Rs.25,000 Correct Answer Incorrect Answer
      C Rs.32,000 Correct Answer Incorrect Answer
      D Rs.43,200 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the principal be Rs. P Rate = 12% p.a. Time = 2 years Simple Interest (SI) = (P × 12 × 2)/100 = Rs. (24P/100) = 0.24P Compound Interest (CI) (semi-annually): Half-yearly rate = 12/2 = 6% Number of half-years = 2 × 2 = 4 CI = P × {(1.06)⁴ – 1} = P × (1.2625 – 1) = 0.2625P Now, CI – SI = 972 ⇒ 0.2625P – 0.24P = 972 ⇒ 0.0225P = 972 ⇒ P = 972 / 0.0225 = Rs. 43,200

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