Uniform Distribution of Deaths September 2014 Q3 (CT5)

[mj94]

What is seemingly a straightforward question has been driving me crazy for a good while now..

Calculate 2.5q75.75 using the method of Uniform Distribution of Deaths.


Basis: Mortality PMA92C20

I understand the method used in the mark scheme but I used the method of interpolating lx values (which I have previously used for other questions) as follows:

2.5q75.75 = 1 - (0.25p75.75 * 2p76 * 0.25p78)
=1*(l76/l75.5)*(l78/l76)*(l78.25/l78)

Simplifying gives:
=1-(l78.25/l75.25)

using the above mortality basis and interpolating:
l78.25 = 0.25*l79 +0.75*l78 = 0.25*7298.223 + 0.75*7615.818 = 7536.41925
l75.25 = 0.25*8168.798 +0.75*8405.160 = 8346.0695

Therefore:

2.5q75.75 = 1 - (7536.51295/8346.0695) = 0.097 as opposed to 0.08404 in the answers?

I'm not sure what it is that I'm missing? Probably something simple but any help will be much appreciated!

 

[Calm]

What is seemingly a straightforward question has been driving me crazy for a good while now..

Calculate 2.5q75.75 using the method of Uniform Distribution of Deaths.
Basis: Mortality PMA92C20

Be careful of careless mistakes. Yes, I also made one in this thread.
The general methodology is correct, but this specific step

l75.25 = 0.25*8168.798 +0.75*8405.160 = 8346.0695

is what's missing, as your l75.75 somehow changed to l75.25 (and the calculation of that is consistent with l75.25), so your answer is effectively finding 3q75.25 instead.