When exactly to use Net Premium Reserve formula for mortality Profit

[Junaid Khan]

When do I use the net premium reserve formula in a Mortality Profit question?

In some questions they first calculate the premium in order to calculate the reserve then the DSAR .. but in Q2 of booklet 10 they use net premium reserve formula.. is this simply because x+n is equal to 65 and it is very easy to just calculate the values using the formula book?

 

[Robert Chadburn]

Your question is more generally asking when you would use this "short" formula (the one on page 37 of the Tables) for calculating the net premium reserve (it doesn't have to be a mortality profit question, though it obviously can be).
You can use this formula for the net premium reserve ONLY for whole life or endowment assurance policies that are paid for by annual premiums. For any other contract, you have to use the full prospective reserve formula (which is the EPV of the future benefits minus the EPV of the future premiums as at the reserving date), for which you would first have to know (ie calculate) what the Net premium is.
The age and duration don't have to add up to 60 or 65 to use this formula! If they do then the numerical calculation is even easier using the tables, because you can use the temporary annuity functions that are tabulated on eg page 100/101, but the page 37 net premium reserve formula will work for any age and duration combination, not just those that add to 60 or 65.