SOLUTION: an Insurance company charges an excess of �500 per policy i.e claiments must pay the first �500 of any claim. In a survey of cars costing �25,000 the following was found for the pr

Question 803009: an Insurance company charges an excess of �500 per policy i.e claiments must pay the first �500 of any claim. In a survey of cars costing �25,000 the following was found for the probability of a claim and the size of the claim.
Total Loss 0.001
50% loss 0.01
25% loss 0.05
10% loss 0.1
Question: What premium should be set to give an average profit of �200 per policy?
this is what I did but I'm not sure if I'm right.
200 = (Premium)(0.999) - (25,000-500-200)(0.001)
Premium = �224.52
I repeated this for the 4 scenarios and got the average premium needed.
Is this correct?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
an Insurance company charges an excess of �500 per policy i.e claiments must pay the first �500 of any claim. In a survey of cars costing �25,000 the following was found for the probability of a claim and the size of the claim.
Total Loss 0.001
50% loss 0.01
25% loss 0.05
10% loss 0.1
Question: What premium should be set to give an average profit of �200 per policy?
---
Let the premium cost be "x":::
-------
You want expected gain (for the company) to equal 200.
----
Random gain values:::::::Corresponding probability
-25000+500+x:::::::::::::: 0.001
-12500+500+x:::::::::::::: 0.01
-6250+500+x::::::::::::::: 0.05
-2500+500+x::::::::::::::: 0.10
+x:::::::::::::::::::::::: 0.939
------
Equation::
(-24500+x)0.001 + (-12000+x)0.01 + (-5750+x)0.05 + (-2000+x)0.10 + 0.939x = 200
=====
-632+x = 200
x = $832
===============
Cheers,
Stan H.

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