Q&A Bank Part 4 Q4.8 parts b) and c)

[Michael_14]

I'm not sure I agree with the solution to this question in parts b) and c). Has anyone else looked at it?

It states emphatically in the notes in section 3.2 of Chapter 13 that:

"if we are told the single decrements are uniformly distributed then we can't use the formula: (i won't retype it but its the one derived in section 2.3), since these are based on the assumption of uniformity in the multiple decrement table."

Isn't this exactly what is done in the solution to this question?

Michael

 

[Julie Lewis]

Michael, you are absolutely right.

The independent rate of withdrawal at age 17 should be calculated using the formula on Page 35 of the Tables (setting the gamma decrement equal to 0 since there are only 2 decrements operating at age 17, namely withdrawal and death). We know that:

(aq)17^(w) = 600/9245

(aq)17^(d) = 5/9245

Using simultaneous equations gives q17^(w) = 0.064918 (which is actually the same as the answer using the wrong method to 6dp).

Part (c) can be tackled in the same sort of way but this time you'd have 3 simultaneous equations and it is algebraically a bit nasty. I doubt you'd have to do it for 3 decrements in the exam.

Thanks for pointing this out. I'll make sure that the notes are changed and I'll put something about this in the CT5 corrections document.