Chapter 14 Q14.17/14.14

In Q14.17 from the notes(Subject 105,April 2000 Q7), It is assumed retirement only takes place at age 65, as the question mentions so.

In Q 14.14(Hard), the question mentions retirement takes place between ages 60 and 65, yet the solution takes into account retirement at all ages after 48.

Could anyone shed any light on this?

Cheers!

 

In Q14.14, there's no need to assume retirement before age 60 and you can do the question just assuming retirement between age 60 and 65. There's a note to this effect at the end of the solution (page 54). Do use yor alternate method if you prefer.

The key is that, although in the derivation we assume the member can retire before age 60, when we come to evaluate the functions by looking them up in the tables, they assume rx=0 for all ages under 60 (ie no retirements are allowed under 60). See the service table on page 142. So all the extra terms we get by assuming you can retire before 60 will disappear when you come to evaluate the functions.

One justification of the method shown is that if you can do that, then you can deal with the most complicated type of benefit (one which is payable on retirement at any age - eg ill health retirement), so it's good practice!

 

Mark,

Many thanks for your reply. I partially understand what you mean! What you said works for past service liability as sMx are the same for x<60.

However, the sR'x are not the same for x<60. From what I understand the future service liability with my method would be sR'60, and not sR'48 as in the solutions. which are clearly not the same.

Could you please clarify further.

Regards

 

Whilst the Mxs are the same for ages under 60, the Rxs are not the same for ages under 60.

Rx is a sum of the Mx terms for each future year of working, so increasing the age will reduce the number of Mxs in the sum and hence change the Rx value.

The form of the solution for the future service liability using your alternate method is given at the bottom of page 54 of chapter 14. Have you looked at that? You end up with an sR60 term to deal with years of working (60,61) through to (64,65) and a set of M60 terms to deal with the years of working from (48,49) to (59,60).

My advice is that you work through the future service liability part of the solution, assuming that you do not allow retirement before age 60 (ie setting each rx=0 for x<60), and aim for that answer. (An attempt on my part to type it out in full here would be fairly incomprehensible due to formatting issues!).

Good luck!

 

Cheers! Think i'm with you now..In that case if the question said retirement was only possible at age 65, what would the total benefit look like? Is it just C65 for past service, and something like the following for future benefit:

=(30000/60)*C65(S48+S49+.....S64)/sD48

I get this as there are no Mx term, just a Cx term for each year of service...

Thanks!Hopefully the last query....

 

Yes - that's right. You've obviously got the hang of it now!

C terms are associated with retirement at single ages, M terms arise where you have a range of retirement ages.

Good work!

M.