Q&A bank q1.12

[12345]

Hello all,

Shouldn't the answer to part (i) consider l30/l25, i.e. the probability of survival to age 30? Similar issue in part (ii).

Thanks in advance

 

[Mark Mitchell]

The factor of l30/l25 is there....It's just upside down!

Let's think first of all of calculating expected present values. Here you have a factor of v to allow for the operation of interest and a factor of npx say, to allow for mortality. Note that both of these factors operate to reduce the value ie. they are both less than 1.

When calculating expected accumulated values, you use the reciprocal of each of these factors, because discounting and accumulation are opposite processes. So in Q1.12 you have a factor of (1+i)^n and another of (1/npx) which turns out to be l25/l30. Note that here both of the factors serve to increase the value ie. there are both greater than 1. This is what you'd expect from an accumulation.

This type of question works best where you have a group of people and a fund of money that is to be divided among the survivors at some future point in time. See April 2006, Question 5 for an example.

 

[12345]

Thanks Mark.

What threw me was the different method used in q4.14 but I've now realised that this method doesn't allow for survivorship in the accumulation.

 

[12345]

No, that's wrong, but I have figured out why it works!