CT1 IFoA Sept 2007 Q11 (iii)

Discussion in 'CT1' started by Janboyd, Apr 7, 2016.

  1. Janboyd

    Janboyd Member

    Please can someone help me with the numerator of the duration of the liabilities?

    100v (1×1 + 1.05v×2 + 1.05^2 v^2 ×3+…+1.05^59 v^59×60) = (1.03/1.05) 100 v (1.05v×1 + 1.05^2 v^2 ×2 + 1.05^3 v^3 ×3+…+1.05^60 v^60×60)

    The part inside the brackets can be regarded as (Ia)60 evaluated at a rate of interest i such that v = 1.05/1.03

    but (1.03/1.05) x100 x1.05v doesn't equal 100v?
     
  2. Muppet

    Muppet Member

    correct, it equals 100. But there are two v's. One outside and one inside the brackets.
     

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