Q & A Part - 2; Question - 2.27

(Part A)The bonus as per the question is being accrued at the end of the year and also as per the solution to the question the benefit payable at the end of the first year is 10000, for 2nd year 10200 and so on. Thus in accordance with this the cumulative amount at the end of the 20th year should be 10000+(19*200)=13800 whereas in the solution it has been given as 14000. Why is this so?
Also what would be the amount of the death benefit for the 20th year?

(Part B) Similarly for this also the benefit at the end of 1st year is 10000, 2nd year is 10000*1.04 and so on so accordingly for the end of the 20th year it should be 10000*(1.04^19) whereas it has been given 10000*(1.04^20). Why is this so?

 

If policyholder dies 20th policy year, that means it will die in time 19-20, i.e. before the 20th bonus announced, So only 19 bonus get accumulated. And for survival 20 bonuses.

For part 1) death Benefit for 20th policy-year is 13800 but survival benefit 14000

 

So we can say that if the bonus is being declared at the end of the year then they are actually being declared after paying off any death benefit but before payment of any survival/maturity benefit?
And also if suppose in this case the bonus was being declared at the beginning of the year then I suppose even the first death benefit payment at the end of the first year would have also been inclusive of bonus for first year and at the end of the 20th year the death benefit as well as maturity benefit would have been equal to 14000 right ?

 

As death occured before declaration of bonus, so Benefit accrued before bonus. So, even the payment is late, the Benefit does not contain the bonus that got declared after acrual of Benefit(although before payment)

 

And what about the case where the bonus would have been declared at the beginning if the year in this case ? Then I suppose both the death benefit and the maturity benefit would be equal?
Thanks for your replies.

 

Yes! For that case, Death Benefit in the last policy year will be same as Maturity Benefit.