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CT5-ASI - Nov 2005 Q.9

R

rsmallela

Member
Can someone explain this solution please?

'Obtain a simplified expression for an annuity due of Rs.30,000 payable annually during the joint lifetime and lifetime of the surivor of (40) and (50) and subject to the provision that it will continue for at least 20 years after the first death and 10 years after the second death'.

Appreciate any help..

Thanks,
Raj
 
any luck yet?

Been trying to figure this out and its hard made me realize Ive a long way to go in understanding ct5.

Em have you looked at the type 6 benefit in ct5 chapter 9

type 6 : an annuity payable to (y) on the death of (x) and continuing for n years after (y)'s death

also the example of Yolanda and Xanthia .

The methods of these questions will come into the solution I feel.
Been trying to think of the terms in the series we will add up to get our expected present value but keep getting tied in knots its very confusing.

so in the type 6 benefit there is the use of a joint life assurance where y must die second and its used as a sort of indicator function ( not only that but as a discount to the time of y death for the guarantee annuity for n years).


in the solution to this question we will prob use 2 different life assurance function as indicators for the 2 mutually exclusive guarantees we have one of 20 years and one of 10 but this brings in as many problems as it solves i think since now we have a problem with the "first terms" in the series we have to add up .
the problems im taking about are the terms after 1 person has died and before the other does. this prob wont make any sense .
also the non symmetry of the ages is giving me grief to ,cant decide what terms i need to include .

Sorry for a pretty useless bit of waffle there Raj but just to let ya know im thinking on it .
Hope a tutor weighs in on this !!!!

edit : thinking now it could even be 4 different joint life function as indicators for the 4 possibilities ie possibility 1 :40 dies first and 50 dies within 10 years . I hope you know the other 3 possibilities im referring to.


One last thing what does Rs.30000 mean ? the Rs. bit?
 
Having a look at it now

I should of posted days ago I was going to ask did you have a solution , suspected you did from wording of your original post . oops.

So it will take awhile for me to figure this out will post tomorrow.
 
Got a chance?

Got a chance to look into the solution??
 
Sorry for no reply

Its just I cant explain it properly cause i dont understand it totally , I was kinda on the right track I was trying to skip straight to the formula at the end of the solution (with all the assurance functions ) without doing the grunt work.

the thing is how ?to convert the diagram in the answer to the probabilites listed ,the bit "for a general payment at time t, we need to consider"

that is the key to the question as all the rest is just algebra , but i cant figure out which part of the diagram goes with what probability , im guessing this as there is 6 probabilities and 6 options a with c , c with a and so on .

So if I figure out which combination of x , y ie a and c goes with which probability Ill scan something in , and hopefully that might clear up some of your issues , I want a tutor to weigh in on this , and give me a formula for doing this in general ie general x , y ages and general lengths of both guarantees n and m not 10 and 20 that would be mega helpful but probably very hard . but test able since we have an answer here with x=40 y=50 n=10 and m=20.

Sorry for no reply its just I stopped studying ct5 after looking at this and decided not to take the exam next month ( and its cause of you Raj and your very hard question ) so i could concentrate on the other 3 im taking that I actually stand a chance of passing, although ct6 gives me nightmares.

Sorry for the lack of any meaningful help.
 
hey...do not worry about it..it's just one off hard question...we may not need to deal with it in our exam....hopefully..

I really wonder how we can request any of the acted tutors to help us in such things...

all the best with all your exams...I am giving CT3 and CT5...in May (India) exams...

Thanks,
Raj
 
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