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    Question

    Aman invested ₹2,00,000 at an annual compound interest

    rate of ___%, with interest compounded every 4 months. If the investment was held for a total duration of 12 months, ________ would be the interest earned by Aman at the end of this period. The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true? I. 18, 38,203.2 II. 15, 31,525 III. 30, 11,230
    A Only I and III Correct Answer Incorrect Answer
    B Only I and II Correct Answer Incorrect Answer
    C Only III Correct Answer Incorrect Answer
    D Only II Correct Answer Incorrect Answer
    E All I, II and III Correct Answer Incorrect Answer

    Solution

    Compound interest = Sum X {1 + (rate of interest/100) }time – Sum Since, the interest is compounded every four months, it is compounded 3 times a year. For I: Effective rate of interest = 18 ÷ 3 = 6% per term Effective time period = (12/12) X 3 = 3 terms So, sum at the end of 12 months = 200000 X {1 + (6/100) }3 = Rs. 2,38,203.2 So, interest earned = 2,38,203.2 - 2,00,000 = Rs. 38,203.2 So, statement I is true. For II: Effective rate of interest = 15 ÷ 3 = 5% per term Effective time period = (12/12) X 3 = 3 terms So, sum at the end of 12 months = 200000 X {1 + (5/100) }3 = Rs. 2,31,525 So, interest earned = 2,31,525 - 2,00,000 = Rs. 31,525 So, statement II is true. For III: Effective rate of interest = 30 ÷ 3 = 10% per term Effective time period = (12/12) X 3 = 3 terms So, sum at the end of 12 months = 200000 X {1 + (10/100) }3 = Rs. 2,66,200 So, interest earned = 2,66,200 - 2,00,000 = Rs. 66,200 So, statement III is false.

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