Hi, i have two questions after read through the solution given. 1. Why is there no premium added for the Asset calculation on immediate annuities. 2. While working on annuity payment of immediate annuities, why is there no need to consider the probability of survival (1-0.035) while for deferred annuities, it did consider the probability of mortality (1%)? Thank you.
Hi Immediate annuities are single premium products. Therefore, for business that is in-force at the start of the year, there will be no further premiums arising. The question states that the information in the first table excludes the new business written during the year. Thus premiums on the immediate annuity business are included within the 33 million new business contribution that is referred to under that table, and which is added on separately to the EV profit calculation (since we are not told how it separates into asset and liability impacts). For the immediate annuities, the first table gives us the amount of annuity benefit that will be paid out, as at the start of the year. The list of bullet pointed assumptions tells us that these annuity payments are made at the start of the year. Therefore there is no need to make any adjustment for survivorship and we can just use the amount given. For the deferred annuities, we are told that they are all still in the deferred period. Any claim would therefore be a death claim during the deferral period, but we are not told the amount of those claim payments. However, we are told what the total in-force sum assured is (ie what would be payable if everyone died). Therefore we need to multiple this by the probability of death. Is that clearer?
