Hi,
The earnings can be deduced from the question.
In 1998 the net written premium was 25 and the earned premium was 10.
So, just for 1998 they earned 40% in the first year.
This is where your assumptions come in to play. It is reasonable to assume that the policies are yearly and earn throughout (not necessarily evenly) the year.
Therefore the remainder of the earnings must be in year two, so 100% - 40% = 60%.
You can then apply the same logic to the next year.
So, they write 50 and earn 35. 15 must come from 1998 (25 written in 1998 and less 10 earned). So from 1999 you earn 35-15 = 20 from what was written in 1999.
Which is equal to 40%, and 60% carries over.
This is the same for all of the years. But it could easily not be 40% year one and 60% year two, depending on the average inception dates and how they are earned out.
The fact that business began on 1/1/1998 means nothing here, except that we have no upr to worry about from previous years.
It would only mean 100% earned in the 1998 accident year if all policies were incepted on 1/1/1998 and lasted a year. This is never stated and we know they only earn 10 so it can't be the case.
You maybe mixing up underwriting and accident years? It is fully earned on an underwriting year basis but earned over two accident years.
I hope this helps.
Last edited by a moderator: Sep 20, 2008
