Chapter 11: Q11.9

[2009]
Another question on reserves...

How do you work out the BOY and EOY reserves on this one in order to arrive at the Cost of Increase in reserves in each of the three years?

Thanks.

 

here you go

took me ages to figure this out , the reserves are worked out via the 7% interest and the number of policies in force at the start of each year .

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Did you check out the original question off the paper that this was based on

http://www.actuaries.org.uk/__data/assets/pdf_file/0009/166329/ExamPapersSubject105_2000-2004.pdf

page 100 , its the same question but different mortality is all.

 

Thanks Hamilton

Your table should be included in the solution

I noticed the EOY CF or Reserves are not brought forward to the next year as opening balance. Is it because in the question there is a comment that reserves are based on one year's office premium?

 

yep

Well we are bringing our reserves forward , but when you go to a new year we have less policies in force ( people died ).

we only ever hold a reserve of P per policy in force , so this is a cost in the first year to set up , but in the second and third year because more people are dying and our reserve is for each policy in force we are releasing reserves in year 2 and 3 , i should of really put a minus sign on year 2 and 3 figures .

lets look at , year 1 to year 2 , closing reserve year 1 is .992P this is chosen as it is the exact amount we need to have a reserve of 1P per policy in force at the start of year 2 .

And going from year 2 to 3 we get interest on our reserve of 1P which brings it up to 1.07P but we know we only need an opening reserve of 1P for year 3 , but only 99.0991% of people survive year 2 , so this implies we can release 0.079P reserves , etc.

Like i said in my last post check out the original question it was based on, the explanation is a bit clearer .

 

Sorry, I still don't quite understand this albeit your long explanation.

I looked at the solution you recommended but there were no explanation besides the table and the examiner's commentary which have no bearing to the reserve calculations.

I guess I'm stuck to the thought that closing balances should be brought forward to the following year as opening balance. So in my head, the opening reserve for year 2, should be 1.992P (which is 0.992P + P). Then the interest earned in year 2 would be 7% of 1.992P

Where have I gone wrong?

 

jensen, the question says that the reserve required is one years office premium "P", hamilton has given a very good explanation! See the reserve is only required for lives who survive, so sure .9920 is held at the end of the 1st year, but only .9920 of these lives are expected to be alive in year 2 so this .9920P is sufficent to hold P at the start of year 2 (.9920P PER .9920 lives = P/policy in force). Your going wrong because your treating the reserves as cumulative [infact the release at the end of year 2 is equal to the interest earned on P + some term reflecting the fact people have died meaning less is needed per policy],only P is required at the start of every year per policy in force, as hamilton says, at the end of year 2, "too much" reserve has been built up, so some can be released, Because only .990991P is required at the end of year 2 to be able to have P for each live surviving till the 3rd year.