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April 2001 Ques 4 (403)

H

Heena

Active Member
A general insurance company writes an extended warranty contract that takes
over from the manufacturers warranty after the product is 12 months old and
extends the warranty until the product is 5 years old. The total insurance
premium is due at the time of purchase of the product. The table below shows
the premium written during underwriting years 1998 to 2000 and the estimated
figure for 2001.
Underwriting Year Written Premium
(£000s)
1998 50
1999 100
2000 100
Plan 2001 100
Calculate the earned premium in 2001, stating any assumptions made.


Ans -
Underwriting Year /. 1998 1999 2000 Plan 2001 Total
Calendar Year.

1998 0 0 0 0
1999 6.25 0 0 0
2000 12.5 12.5 0 0
2001 12.5 25 12.5 0 50.0
Assumptions: No Premium earned in first year, any other is wrong
Premium earned evenly (or some reasonable assumption) over next 4 years
Answer is 50.0 (or whatever is consistent with earnings assumptions)
Business is written evenly over the year.
No business written prior to 1998 (or if so then answer will be different)
///////////////////

Can anyone please explain the solution e.g. why does the earned premium is 6.25 in 1999 (of the premium written in 1998), similarly why the written premium of 1999 has earned premium of 12.5 in 2000 and not 2005?
 
For business written in 1998, the average policy is written in mid-1998. That average policy will not come on risk until a year later, in mid-1999. So it will be exposed to risk for:
- half of 1999 (ie from 1st July to 31st December 1999)
- all of 2000
- all of 2001
- all of 2002
- half of 2003 (ie from 1st January to 30th June 2003).

So you can see that 1/8 of the risk occurs in 1999. This gives us 1/8*50=6.25 earned premium during 1999, in respect of business written in 1998.

This should give you enough of a clue to attempt the question again. Have another go and see how you get on.

I've knocked up an answer in the spreadsheet attached.
 

Attachments

Thank you so much, this was extremely helpful!
One more thing , would it be fair to assume that all policies are written at the start of the year (like e.g. start of 1998)? so that would make exposed for risk look like
- all of 1999
- all of 2000
- all of 2001
- all of 2002
or is it better to assume mid year?
 
That would be a very simplistic method Heena, I doubt you'd get a mark for it.

The examiners routinely assume that policies are written evenly throughout the year (and hence, the average policy is written mid-year). I recommend you always make that assumption unless you're explicitly given other information in the exam.
 
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