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#1
02-05-2020, 06:29 PM
 JohnTravolski Member Non-Actuary Join Date: Aug 2016 Posts: 66

I am struggling with the following problem:

Given the following expenses, calculated the premium discount for a \$10,000 standard premium risk:

Assume the profit provision is 5% and the tax provision is 5%.

The provided solution is:
[(4000)(0.2+0.1-0.15-0.05)+(5000)(0.2+0.1-0.1-0.05)] / [(1-0.05-0.05)(10000)] = 0.128

This is confusing to me and don't understand what the numerator in the solution represents. Can somebody walk me through how the numerator is obtained (and what each term represents)?
#2
02-05-2020, 07:21 PM
 laprimony CAS Join Date: Sep 2016 Posts: 4

The numerator is coming from
1. The dollar amount of the risk that is within the range, multiplied by
2. the difference between the total expenses in the lowest range (in this case first 1000) and the total expenses in the range we are looking at.That is, the expense reduction from the lowest (base range) to each of the other ranges.
So the way they did it here, the first range total is 20% + 10% = 30%
Now subtract range 2 total from 30% and range 3 total from 30% i.e
(30% - (15%+5%))=10% and that's what you will multiply by the amount from the risk in the range, which is 4000
For the last range, do the same:
(30%-(10%+5%))=15% and multiply that by the amount for the risk that is in that range, so in the base we had \$1000, the second range has the next 4000, so it means the last range has 5000 to total the risk's \$10000 standard premium
In the source material they would add the profit and tax to total expenses but it won't matter since it is being subtracted out anyway.
Hope that makes sense. I can attach an excel workbook too if that would help.
#3
02-08-2020, 05:51 PM
 JohnTravolski Member Non-Actuary Join Date: Aug 2016 Posts: 66

Thank you, this was very helpful. I understand it a lot better now.

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