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      Question

      The difference between compound interest and simple

      interest on a sum for 2 years at 10% per annum, when the interest is compounded annually is Rs. 25. If the interest were compounded half yearly, the difference in two interests would be:
      A Rs. 38.76 Correct Answer Incorrect Answer
      B Rs. 26.90 Correct Answer Incorrect Answer
      C Rs. 31.60 Correct Answer Incorrect Answer
      D Rs. 32.40 Correct Answer Incorrect Answer

      Solution

      For 2 years, difference between compound interest and simple interest is: Difference = Principal × (Rate/100)² So, 25 = Principal × (10/100)² 25 = Principal × 1/100 Principal = Rs. 2500 Now, if interest is compounded half-yearly, Rate = 10/2 = 5% per half-year Time = 2 × 2 = 4 half-years Compound Interest = 2500 × [(1 + 5/100)⁴ – 1] = 2500 × [(21/20)⁴ – 1] = 2500 × [(194481/160000) – 1] = 2500 × (34481/160000) = Rs. 538.765625 Simple Interest = (2500 × 10 × 2)/100 = Rs. 500 So, required difference = 538.765625 – 500 = Rs. 38.765625 Therefore, the difference between compound interest and simple interest is Rs. 38.76 approx.

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