CT5- September 2006 Question 10

Helloo. Just wondering, what is the intuition behind the first part of the solution on Page 80 of Revision Notes Booklet 3:

V(1)= 175,000 + 10,000 (1- (a˙˙70/a˙˙46))
[=reserves on 31/12/05 + sum assured x tVx]

^I don't understand why we are multiplying the sum assured with what I assume to be 24V46

●Why not just add the sum assured only since that is what the company would be paying out to that one person who is dying?
●Why is it not a˙˙69/a˙˙46?
●Is it just me or is this question really confusing?

Thanks to anyone who can help!

 

The solution is trying to work out the reserves at the end of the year for all policies in force at the start of the year. The first group are those who were aged 69 at the start of the year. Now we know that the total reserves for those who survived the year was 175,000. However, there was another policy also in force at the start of the year, who died during the year. This was the policy with the sum assured of 10,000. We know this because the entry age of 46, plus the number of years from entry (1.1.82) to the start of 2005, comes to 69. We need to include the reserves for this policy along with the others, because for the mortality profit we need to include all the policies that were in force at the START of the year, and this includes the one that died.
So, the reserve for this policy has to calculated using the net premium reserve formula. Using this formula, in the annuity in the numerator we need the age at the reserving date, which is 70, and the age at entry, which was 46.
Your first bullet you seem not realise that we are calculating the reserves to USE in the death strain calculation, not the amount paid on death during the year.
To answer your second bullet, the reason it is not 69 in the numerator is that we need the reserves at the end of the year, not the start, when we calculate the death strain.
For your third bullet? - this was a hard question and takes some sorting out!
Hope that helps. Sorry you've had to wait to get a reply.
Robert