"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

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

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