September 2016 Q9

Can someone please explain me why do we have the term 125000b * v^35 * 35p[30]?

 

the reason is as follows;
in the solution it was supposed to be 125000(1-b)(A[30]:35 temporary assurance) + 125000b *(IA[30]:35 temporary assurance)
+ (125000+125000*35*b*(A[30]:35 pure endowment))

instead of taking temporary assurance they took endowment so let me show you how they balanced the things

add 125000*(1-b)*(A[30]:35 pure endowment) and subtract 125000*(1-b)*(A[30]:35 pure endowment)

so added part of 125000*(1-b)*(A[30]:35 pure endowment) will be combined with 125000(1-b)(A[30]:35 temporary assurance)
and it formed 125000(1-b)(A[30]:35 endowment)

now let us simplify the subtracted part
-(125000*(1-b)*A[30]:35 pure endowment) = -125000*A[30]:35 pure endowment + 125000b*A[30]:35

let us also break the pure endowment part which i wrote in first line
125000*(A[30]:35 pure endowment))+35*b*(A[30]:35 pure endowment))

so as you can see -(125000*A[30]:35 pure endowment of subtracted part got cancelled with 125000*(A[30]:35 pure endowment)
and from subtracted part only 125000b*A[30]:35 was left so that is how we got 125000b*A[30]:35 which is same as 125000b*V^35*35p[30]

 

here is the solution

 

In an exam setting is this simplification necessary. I try to brute force the general form using the term assurances

 

yes you can adopt whatever method is convenient, like here in this question examiner tried to balance the things by introduction 125000b * v^35 * 35p[30], but there are other ways of doing it.

when i solved this question question so i took b as bonus amount than taking b as bonus rate so that was more easy

 

That's exactly what I did