2002 Exam #17b

[Tu_Kewl]

Can someone explain this answer.

The all10 manual formula doesn't give the correct answer and the exam solutions give me a formula I don't really understand.

Can someone explain how to get the 1.0529 in the usual parallelogram method so that when you divide .935/1.0529 you get .888?

Thanks

[Super Silver Haze]

This doesn't directly answer your question, but all they're asking for is what the earned premium from the experience period would be at current rate levels.

The rate per exposure on 1/1/99 was $120. Current rate would be 120 x 1.1 x .85 = $112.20.
The experience period is 1.5 years. 200 exposures were written per year, so 300 exposures were earned during the experience period.
So the experience on-level earned premium is just $112.20 x 300 = $33,660. You don't even have to use the parallelogram method for that question.

This is reflected at the end of the exam solution, when they say
"or current rate x earned exposures = 300 x 120 x 1.1 x .85 = $33,600".

Does that help?

[Tu_Kewl]

Can you explain how you get 300 and 120 for exposures?

[Super Silver Haze]

200 exposures are written every year. The experience period is 1/1/00 to 6/30/01, which is 1.5 years. In 1.5 years, you'll have 200 x 1.5 = 300 earned exposures.

$120 is the rate per exposure as of 1/1/99. It's given in the question.

[Tu_Kewl]

Ok that is really simplified the 200 * 1.5

but if the exposures weren't 200 in each year, then that number couldn't be calculated in that way.

Can you give me the breakdown by each AY please?

they have 100 from 99
100 from 00
75 from 00 at different rate
25 from 01

[Super Silver Haze]

Check the picture below. It's the diagram from the exam solutions, I just changed it a little.

Red parallelogram is year 1999 policies
Yellow parallelogram is year 2000 policies (light yellow before the +10% change, dark yellow after)
Blue parallelogram is year 2001 policies
And the purple rectangle is the experience period.

Each parallelogram represents 200 earned policies.
1/2 of the red parallelogram is in the experience period, so you get 200 * 0.5 = 100 for year 1999.
1/2 of the yellow parallelogram is in the experience period and before the 10% rate change, and 3/8 of it is in the experience period and after the 10% change.
So you have 200 * 0.5 = 100 policies for year 2000 from before the rate change, and 200 * 0.375 = 75 policies from after the rate change.
And 1/8 of the blue parallelogram is in the experience period, so 200 * 1/8 = 25 policies come from year 2001.

[Tu_Kewl]

That makes sense...thanks...