Sep 2017 q 13 - somebody please help!

13. (ii)
Can someone please explain why the reserve equation at the end of the 17th policy year 17V is 50000(1.0192308)^16...... and not ^15 as we have to divide the whole thing by 1.0192308 one more time to get the term assurance function from 6% to 4% interest?
[In the question, at t=1, the benefit payable is 50000, at t=2 it is 50000x1.0192308, and so on, at t=n it is 50000x1.0192308^(n-1)]
Thanks!

 

I get the sense that since there are 16 increases between (date of first increase) 1-Jan-2001 and 1-Jan-2016 (date of last increase before reserve calculation at the end of the year), death benefit in the 17th policy year (1Jan16-31Dec17) is 50000*1.01982308^16. There is no need to divide by 1.01923 as it is an increase that must happen by default (only exclusion is for 1st policy year). If you think about it, the 17th policy year should have 16 increases if the 1st policy year did not get an increase. So in part 3, if you are calculating reserve at the end of 16th policy year (31 Dec 2015), the benefit in the 16th must have 15 increases so 50000*1.01923-8^15. Hope this helps

 

Thank you for your reply Sid! Much appreciated.
Yes I understand up to that part, where the payment for the 17th year is 50000x1.019238^16. However in part (i) when calculating the net premium, the whole thing gets divided by 1.019238. Why doesn't that apply anymore? Since at time 17, payment is 1.019238^16 but the discount factor is v^17?

 

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When calculating reserves at t=17, you will look at future year benefits which will be with factors v*1.01982308*q57 +v^2*1.0192308^2*p57*q58 +..... therefore no need for dividing by 1.0192. As mentioned 1.0192 dividing is only needed at the policy outset to compensate for the 1st year for which there is no increase. I wouldnt assume the discount factor (v^) and 1.0912^ to follow the same relationship as done at the outset (where you need to divide by 1.019 to get the v^ to match the power on 1.0192). It resets at every future date when reserve calculations are done and needs a reassessment (ie. at t=17 you reassess how the increase to benefits and the discount factor applies, which in my understanding is as explained). Hope it helps.

 

Ohhh yes that makes sense, finally got it. You explained it really well. Thank you so much!