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Mortality Projection

A

Actuary@22

Very Active Member
Hi
In the ques given on pg 32,I followed the same steps that were used at age 65 for calculation at age 66.

Since 10% of deaths are due to cancer 10%*2097
d'66=2097-209.7=1887.3
So q'66= 1887.3/77353=0.02439
And then l'67=l66-d'66=77353-1887.3=75466

But my answer for l'67 doesn't match with the books answer i:e 75560..
Pls explain on why my approach isn't correct.
 
Hello

There are a couple things going on here. Firstly, l'67 = l'66 - d'66 and not l66 - d'66, so you need to use 77450 and not 77353.

Secondly, 2097 is no longer the correct starting figure for the number of deaths at age 66. This is because the population alive at age 66 exact is now different given that the death rate changed for age 65. The 'correct' starting figure for the old number of deaths is:

2097 * 77450 / 77353 =~ 2100.

Or, another way to see this, is that 77450 * 0.02711 (l'66 * q66) =~ 2100. The slight rounding differences is due to the rounded q66 figure. This added complication is why it is generally easier to directly adjust q66 instead (as the notes do).

So, we then have new deaths as 2100 * 0.9 =~ 1890.

So l'67 = l'66 - 1890 = 77450 - 1890 = 75560 as per the notes.

Hope this helps

Andy
 
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