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    Question

    A woman invested Rs. 75,000 at compound interest of 12%

    p.a. compounded annually for 1 year. If the interest had been compounded semi-annually, how much extra interest would she have earned?
    A Rs.500 Correct Answer Incorrect Answer
    B Rs.750 Correct Answer Incorrect Answer
    C Rs.645 Correct Answer Incorrect Answer
    D Rs.900 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Amount = Principal X {1 + (rate/100)}ᵀᶦᵐᵉ ᴾᵉʳᶦᵒᵈ

    So, compound interest = Amount - Principal

    When compounded annually:

    Amount at the end of one year = 75000 X {1 + (12/100)}¹ = Rs. 84,000

    Interest earned = 84000 - 75000 = Rs. 9,000

    When compounding semi-annually:

    Effective rate = 12 ÷ 2 = 6%

    Effective time = (12/12) X 2 = 2 periods

    Amount = 75000 X {1 + (6/100)}² = Rs. 84,645

    Interest = 84645 - 75000 = Rs. 9,645

    Required difference = 9645 - 9000 = Rs. 645

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