To determine the total annual premium for a 19-year-old female purchasing insurance, let's follow these steps:
1. Identify the premiums for each type of insurance:
- Bodily Injury Liability for [tex]\( \$50 / 100 \)[/tex] is [tex]\( \$310 \)[/tex].
- Property Damage Liability for [tex]\( \$50 \)[/tex] is [tex]\( \$245 \)[/tex].
- Collision Insurance with a [tex]\( \$500 \)[/tex] deductible is [tex]\( \$148 \)[/tex].
- Comprehensive Insurance with a [tex]\( \$250 \)[/tex] deductible is [tex]\( \$85 \)[/tex].
2. Calculate the total annual premium by summing all the individual premiums:
[tex]\[
\text{Total Annual Premium} = \text{Bodily Injury Premium} + \text{Property Damage Premium} + \text{Collision Premium} + \text{Comprehensive Premium}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total Annual Premium} = 310 + 245 + 148 + 85 = 788
\][/tex]
3. Consider the rating factor for a 19-year-old female, which is 145.
4. Adjust the total annual premium by the rating factor:
[tex]\[
\text{Total Annual Premium Adjusted} = \text{Total Annual Premium} \times \left( \frac{\text{Rating Factor}}{100} \right)
\][/tex]
Substituting the values:
[tex]\[
\text{Total Annual Premium Adjusted} = 788 \times \left( \frac{145}{100} \right) = 788 \times 1.45 = 1142.6
\][/tex]
So, the total annual premium for a 19-year-old female will be [tex]\( \$1142.60 \)[/tex]. Consequently, her base total annual premium without adjusting for the rating factor was [tex]\( \$788 \)[/tex].
