Chapter 17, Question 4

Why are the annuities in the RV for phases 2 & 3 of the policy in advance (not arrears)?

I think a mis-understanding of the domains of the Kx's is leading me to this question, so if someone could clarify that too, it would be appreciated.

Thanks

 

In phase 2 they are discounting using K+1. K would be the start of the year of the death and so K+1 is the end of the year of death. The first payment is on the next policy anniversary and so this would be an annuity in advance from K+1.

It's similar in Phase 3 when the annuity starts the day after time 25 and the discounting is from 25 (using v^25).

 

You can use annuities in advance or arrears for phases 2 and 3, provided that the v terms used have the correct powers (as Jumper pointed out).

It might sound silly, but for questions like this I find it really useful to draw pictures of what's going on. When I looked at phase 2 of this question I first drew out a timeline so I could figure out when the payments are happening, then drew an example scenario so I could calculate how many payments are being made in terms of Kx.

This then gives me the term of my annuity and I can then choose whether I want to use an annuity in advance or in arrears (both are correct as long as the v term has the correct power - see below).

I've attached my scribbles: