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need help in method of non-integral ages

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  • need help in method of non-integral ages

    "Given the following excerpt from a life table, find the median of future lifetime for a person aged 50 assuming constant force... here are other given details:"

    l_50 = 80000, l_74 = 42693, l_75 = 40280 l_76= 37480

    What I did is I used tP50 = l_(50+t)/l_50 = 1/2. Then, l_(50 + t) = 40000.

    ln l_(50 + t) = ln 40000

    Then using the constant force assumption,

    (1-t)ln l_50 + tln l_51 = ln 40000.

    So, my only problem here is to find the value of l_51... which I got it by using the method of non-integral ages between l_50 = 80000 and l_74 = 42693, l_50 and l_75 = 40280, l_50 and l_76= 37480. I took the average of all the values of l_51 obtained from these three.

    for example, between l_50 and l_74, l_51 = l_(50 + 1/24), then I used l_50^(1-t) + l_74^t, where t = 1/24.

    Using the average value of l_51, I got 25.1234793 to the main formula to find for the value of t, .... but I don't think this is correct.... I was wondering what went wrong.... because the book says its 25.096819... I mean there's a reason how the author got that answer...

    Please help me

  • #2
    Your making the problem to complicated.

    The median future lifetime is when tPx = .5

    Solve,

    tPx = 25P50 * tP75

    Solve for t where the cfm is for the integral age between 75 and 76

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