DP-GH 2008 Exam #1a

[Chris100]

I am reading the solution to this problem and can't understand the SOA's arithmetic.

Premium for each carrier = claims/(1 - admin - profit - tax)*(demo factor).

Carrier 1 has:
claims = $200
admin = 13% of premium
profit = 4% of premium
tax = 1.5% of premium
demo factor = 1.1

It this not 200/(1-.13-.04-.015)*1.1 = $269.94?

The solution says $223.09, and seems to come up with different premiums for Carriers 2 and 3. Does anyone know whether this solution is known to be incorrect, or whether I'm doing something wrong here?

[MATE Seminars]

The values they ended up with were correct, but it appears the formatting from the candidate's answer didn't get transcribed correctly. Also, the demographic factors for carriers 2 and 3 were copied over incorrectly.

The following is what the answer should look like:
The numerator of the formula should be claims divided by demographic factor.
The denominator should be the loss ratio (1 - admin & commission - profit - tax).
Carrier 1: (200 / 1.10) / (1 - 0.13 - 0.04 - 0.015) = 223.09
Carrier 2: (180 / 0.98) / (1 - 0.13 - 0.03 - 0.015) = 222.63
Carrier 3: (220 / 1.25) / (1 - 0.12 - 0.02 - 0.015) = 208.28

Note that an alternative would be to move the demographic factor to the denominator, in which case it is multiplied by the rest of the denominator.

[Chris100]

Thanks, Mark.