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    Question

    An investor put a sum at 14% per annum for 2 years

    compounded annually. If instead the interest was compounded half yearly, he would have earned Rs. 112 more. What was the amount he invested?
    A Rs.12500 Correct Answer Incorrect Answer
    B Rs.12500 Correct Answer Incorrect Answer
    C Rs.10000 Correct Answer Incorrect Answer
    D Rs.12000 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the principal be Rs. ‘P’.

    When compounded annually:

    CI = P(1 + 14/100)² – P = P[(1.14)² – 1] = P(1.2996 – 1) = 0.2996 × P

    When compounded half-yearly:

    CI = P(1 + 7/100)⁴ – P = P[(1.07)⁴ – 1] = P(1.3108 – 1) = 0.3108 × P

    According to the question:

    0.3108 × P – 0.2996 × P = 112

    0.0112 × P = 112

    P = 112 / 0.0112 = Rs. 10,000

    Therefore, the invested amount is Rs. 10,000

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