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    Question

    Study the following information carefully and answer the Questions given below:

    Quantity I. In what time will Rs. 48,000 amount to Rs.

    52,920 @ 5% compound interest?       Quantity II. In what time will Rs. 50,000 amount to Rs. 53060.40 @ 4% compound interest payable half-yearly?  
    A Quantity I < Quantity II Correct Answer Incorrect Answer
    B Quantity I > Quantity II Correct Answer Incorrect Answer
    C Quantity I ≤ Quantity II Correct Answer Incorrect Answer
    D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    E Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer

    Solution

    Quantity I. A= P[1+ R/100]t ⇒ 52,920 = 48,000 [1+ 5/100]t       ⇒ 52,920/48,000 = [ 21/20]t ⇒ 441/400 = [ 21/20]t       ⇒  [ 21/20]2   = [ 21/20]t  ∴  t= 2 years  Quantity II. Since interest is compounded half-yearly, R =4/2=2% p.a. and T  =2xt = 2t  years A= P[1+ R/100]t⇒ 53060.40 = 50,000[1+ 2/100]2t                            ⇒ 53060.40/50,000 = [ 102/100]2t ⇒ [ 51/50]3 = [ 51/50]2t                            ⇒2t = 3 yrs ∴  t = 3/2 years Hence Quantity I > Quantity II

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