April 2009 Q5 (iii)

Discussion in 'SP5' started by newkid, Sep 15, 2020.

  1. newkid

    newkid Ton up Member

    Can someone explain how the answer are calculated, both acted revision notes and the examiners report just go from formula to answer without showing the steps in between - for instance i can see the 2 year bond in calculated using a quadratic equation - however not only does this take time, it's also very difficult to do for 3 years and say 4 years - so i assume there is a much quicker way which i'm obviously missing.

    Just to add if using Taylor's approx

    5.4/(1.055) + 105.4/(1+x)^2 = 100, where x is zC2
    5.4/(1.055) + 105.4/(1+2x) = 100
    5.1184 +105.4/(1+2x) = 100
    105.4/(1+2x) = 94.8815
    105.4 = 94.8815 * (1+2x)
    105.4 = 94.8815 +189.763x
    10.5185 = 189.763x
    x = 0.0554 ~ 5.55%

    As you can see, that gives zC2 of 5.55%, whereas C2 is 5.4% - so this doesn't make sense - the answer should just be below 5.4% so i'm failing to see what is wrong?
     
    Last edited: Sep 15, 2020
  2. Gresham Arnold

    Gresham Arnold ActEd Tutor Staff Member

    Hi, I think you have done the hard work here

    I agree with 5.4/1.055 + 105.4/(1+x)^2 = 100

    So, 105.4/(1+x)^2 = 100 - 5.4/1.055

    = 105.4/(1+x)^2 = 94.8815

    So 105.4/94.8815 = (1+x)^2

    so (1+x)^2 = 1.110859

    So x = 1.110859^0.5 -1 = 5.397%
     

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