# DSAR with death benefit payable immediately

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Good day

Why is the benefit payable 50000 and not 50000(1.04)^0.5 in (iii) when calculating DSAR, since the benefit is payable immediately on death as stated in the question? The reserve in (i) is -41.71.

by (2.9k points)

I believe it is because you are trying to work out the actual profit/loss of the company. So, if you paid for 50,000 in the middle of the year, it wouldn't make sense for this amount to incur interest as you paid for it and now it's gone.

So, the death strain is 50,000 because that is the amount that you actually paid out during the year on death during the first 5 years. If you were to multiply by the interest, that wouldn't make sense because you are inflating the cost of the amount for no reason? It's just adding half a year of interest for seemingly no reason (although there is an argument to be made for this interest representing the interest the company could have made if they didn't have to pay for the benefit but this does not come up in this kind of question when addressing the mortality profit or loss as you are trying to work out the actual profit and loss of the company).

The important time to adjust for interest is when the mortality, which is assumed uniform over the year thus seeing the average time of death occurring halfway through the year, is out of alignment with the payment of the benefit payment. Since the assumed average time of death is halfway through the year, and the average payment is assumed to occur halfway through the year, the no adjustment needs to be made to the benefit amount with respect to interest.

UPDATE: Please see last comment of mine about test conditions at the bottom of the page so you follow 's approach!
by (1.1k points)
edited by

Hi, in the notes they advise that we should make provision for the fact that the benefit is paid immediately (see attached extract). Also, in some other past papers, they do multiply by (1+i)^0.5 when the benefits are payable immediately. Why does this not apply here? Could it be an erroneous omission on the memo?

by (2.9k points)

I might be wrong, so please check the examples in past exam/test questions where they adjust for this part of the interest, but I think it's because they want the mortality profit/loss during the year (i.e. halfway through the year) and not the mortality profit/loss at the end of the year (which I think is assumed in ActEd).

Would you mind checking the examples in other past papers (and not the notes) so confirm my suspicion?

by (1.1k points)

Thanks...There is a similar question where they wanted the mortality profit for the year, and they did multiply by (1+i)^0.5. I'm still a bit confused on how 'during the year' implies halfway through the year, as I interpreted it to mean 'for the 2009 year'. If it is calculated halfway during the year, why don't we use 0.5q59 and t+0.5V instead, and why do we not account for the proportion of the total deaths during the year that occur in the second half of the year, but subtract the whole 20 instead?

by (2.9k points)

If my hunch is correct, then the logic for this is as follows:

- You are assuming deaths occur uniformly throughout the year, so halfway through the year the deaths will occur. Payment happens and, if it's profit/loss for the year, you accumulate that amount to the end of the year (since, as we have always assumed, death occurs halfway through the year).

- We are doing exactly the same thing we have always done. The assumptions are the same except that they want the profit/loss for the year (meaning that when they do their valuation, they want to know their profit/loss for mortality. Valuations usually happen at the end of the year depending on the product but it is assumed for contingencies that valuations happen on a yearly basis unless otherwise stated).

Hence why for the year could be interpreted to mean end of the year.

For during the year, the idea is that profit/loss is arising continuously throughout the year. So, assuming this, profit for the year would, on average, be realised in the middle of the year according to our assumption (because profit or loss is realised on the death, which is assumed to occur uniformly throughout the year resulting in profit/loss occurring, on average, halfway through the year).

That being said, I am going to confirm my suspicion with Logan (my logic in my head seems to make sense but just want to confirm it).

by (1.1k points)
Thank you, so in the case of during the year, the only component that changes is the benefit payable in the DSAR, and everything else stays the same? If the death benefit was paid at the end of the year instead, then would we have to discount it by 6 months, or does it not make sense to calculate mortality profit halfway throughout the year at all in that case?
by (2.9k points)

In that case, I would say yes. and then yes, if the payment was at the end of the year and you were asked for during the year insinuating that they want the value in the middle of the year, you would discount it by half a year.

BUT

Like I said initially, this was a hunch I had. So I have consulted with Logan because he is the one who will be testing this in your exam and he says that he thinks your approach is correct (i.e. following the notes) and if you do that approach in the exam then you'll be correct (and noting that this other approach is done in a few previous examples including a previous UCT test with no clear reason behind why it is followed). So maybe I am right with my hunch and maybe I am not but the more important point is below:

I think it's safe to say that for the exam (and anyone reading this in the future), you should follow the method in the notes outlined by

by (1.1k points)
Thanks for the help Murray, I really appreciate it!!