CM1 April 2021 question 7 - reversionary bonus

[Danny]

Hi,

From looking at the solution to this question, it seems to be the case that the reversionary bonus only applies to the death benefit i.e the term assurance component of the endowment assurance, and not the pure endowment component. Why is this the case? From reading the wording of the question this isn't obvious to me and as far as I am aware, in general, reversionary bonuses can also be paid on the maturity benefit.

If a question comes up like this in future, as it currently stands I wouldn't be able to distinguish whether the expectation would be to only apply the reversionary bonus to the death benefit, to the survival benefit, or to both. This is what I need clarification on because I think I'm missing something here!

Thanks

 

[Danny]

I think I misunderstood what the solution was implying.

For this question, do we have 1/(1+b) multiplied with the term assurance component and not for the pure endowment component because we want to divide by the bonus rate to take one year off of the compound bonus applied to the death benefit, as opposed to the survival benefit which will always get the full bonus? I think the keywords here are vesting at the end of the policy year but I just want to be absolutely clear of my understanding on this.

Does this then mean that if bonuses vested at the start of the policy year, you could evaluate the EPV of any death benefit with these bonuses such as a whole of life assurance or a term assurance as just A_x or A_(x:n) @ j%, where j=(1+i)/1+b -1? I.e you wouldn't need to multiply by 1/(1+b)?

 

[Joe Hook]

Hi Danny,

Yes this is correct. If bonuses vest at the start of the year we already have the first term of the death benefits in the form S*(1+b)*v*prob (ie powers of (1+b) and v match) so we can evaluate this as a level term assurance at the adjusted interest rate (1+i)/(1+b)-1 as you say.

Joe