CT5: Q&A Bank Part 2: Q2.3

I had a look at the answer and don't understand why the premium is added to find the net premium reserve?

Thanks.

 

The convention for calculating provisions is that they are calculated at the policy anniversary before any premiums due then are received. The question asks you to calculate the provision at the policy anniversary after the premium has been received. The answer therefore calculates the policy reserve before the premium has been received and then adds the premium that has been received.

You may also try to understand it from the recursive relationship between provisions. The provision changes because of interest and premiums earned and also benefits paid out. As stated above we have calculated the reserve before any premiums have been paid following convention. In this case we have only received a premium (no interest earned or benefits paid out) so add the premium to the reserve we calculated.

Best wishes

 

Just to clarify, are you saying that if the question had been "calculate the net premium reserve on 30 Jun 2004" on the 5 year anniversary after the policy was issued, the answer would just be the usual net premium reserve?

But because the question ACTUALLY asks for "calculate the net premium reserve on 1 July 2004 assuming all premiums due by that date have been paid", we have to add the premium to the net premium reserve?

I think the reason why I am baffled is because net premium reserve = prospective reserve which looks at FUTURE income & FUTURE outgo. If a premium has been paid already, it's no longer FUTURE income, so why should we be adding it to the usual net premium reserve to get the answer??

Hope someone can shed light.

 

I read ziv's explanation but I'm afraid I'm still confused.

Net premium reserves are calculated by using the prospective reserve which looks at FUTURE income and outgo. I understand that the premium has just been paid (on 30 June 2004) but because it's just been paid, this is no longer FUTURE income, so why should it be added to the usual net premium reserve when working out the "new" net premium reserve???

Really appreciate it if anyone can shed any light. I've stared at this for ages, even gone back to the derivation of prospective reserve etc.

Just to clarify... is the net premium reserve quite different if calculated on the 5 year policy anniversary (30 June 2004) compared to at 1 July 2004 as in this question? Seems that's what the question is saying.

 

It is a matter of a double negative

Hi MissAussie; It is a matter of a double negative which becomes a positive

Example

Normal WLA contract NP reserve calc

S*Ax+t - P*annuitydue_x+t (1)


Calculation in your special case WLA contract NP reserve calc:


S*Ax+t - P*(annuitydue_x+t - 1) (2)
= S*Ax+t - P*annuitydue_x+t + P (3)

Note the P at the end is what Ziv is talking about. If you look closely
(3) = (1) + P

Note (2) is effectively

S*Ax+t - P*annuity in arrears_x+t (4)

(4) can be a step before (2) if you like

 

Great explanation, thanks heaps. I see now that I was getting confused because of the negative sign in front of the Premium.

And sorry for the double post, I didn't realise the posts were now moderated... I thought my 1st one got eaten!