There is an FKK Indemnity that insures automobile liability risk for data scientists. There are two rating classes, Honda and Toyota. The Base Rate for Honda is 300 for 6 months at basic limit of 25,000. And for Toyota the Base Rate is 500. In addition there is a policy fee of 50 for agent's commission. Most data scientists buy up the limit of liability to 1,000,000. The increased limit factor for this is 4.00.
Question is asking how much more does Toyota owner pay compared to Honda for this $1,000,000 policy?
I currently assumed to multiply (Base Rate * Limit Factor) + Fees, to find each owners cost. Was not sure how the limit of the liability is utilized in the equation that insurance companies use. The difference I got was $800. But I'm not confident, because I feel the liability limit needs to be considered.
The fees are the same regardless of the rating class, so the premium difference between the two rating classes does not depend on the policy fee.
The rating factor is the adjustment for the increase in liability limit. In other words, the base rate is multiplied by the rating factor corresponding to the limit of liability that is desired by the policyholder. The resulting premium does not depend on the actual amount of the liability limit in any other way; this is how basic ratemaking works. For instance, a rating plan might have a table of rating factors like this:
$$\begin{array}{c|c} \text{Liability Limit (thousands)} & \text{Rating Factor} \\ \hline 5 & 0.75 \\ 10 & 0.85 \\ 25 & 1.00 \\ 50 & 1.25 \\ 100 & 1.50 \\ 250 & 2.50 \\ 500 & 3.00 \\ 750 & 3.50 \\ 1000 & 4.00 \\ 2000 & 5.00 \\ \end{array}$$ where each rating factor is calculated from historical adjusted loss expenses in such a way that the expected value of premiums minus losses is positive (so the book of business should remain solvent unless future losses are in excess of historical ones). So if a policyholder wants to reduce their coverage below the base rate of $25000$, they get a premium discount determined by how much reduction in coverage is applied; and if they want to increase their coverage, the premium is correspondingly increased by a factor that is determined by historical exposure to loss.
Therefore, all you need to do is compare the base rates for each rating class multiplied by the rating factor for the corresponding selected liability limit. Since the difference in base rates is $200$, the difference at a rating factor of $4.00$ for a limit of $1$ million is simply $4(200) = 800$.