A 21-year-old female driver buys [tex]$25 / 50 / 50$[/tex] liability insurance, collision insurance with a [tex]\$ 500[/tex] deductible, and comprehensive insurance with a [tex]\$ 250[/tex] deductible.

What is her total annual car insurance premium?

Liability Insurance
\begin{tabular}{|c|c|c|}
\hline
Type & Amount & Premium \\
\hline
\multirow{3}{*}{\begin{tabular}{l}
Bodily \\
injury
\end{tabular}} & [tex]$25 / 50$[/tex] & [tex]$\$[/tex] 220[tex]$ \\
\cline{2-3}
& $[/tex]50 / 100[tex]$ & $[/tex]\[tex]$ 310$[/tex] \\
\cline{2-3}
& [tex]$100 / 300$[/tex] & [tex]$\$[/tex] 450[tex]$ \\
\hline
\multirow{3}{*}{\begin{tabular}{l}
Property \\
damage
\end{tabular}} & $[/tex]25[tex]$ & $[/tex]\[tex]$ 175$[/tex] \\
\cline{2-3}
& [tex]$50$[/tex] & [tex]$\$[/tex] 245[tex]$ \\
\cline{2-3}
& $[/tex]100[tex]$ & $[/tex]\[tex]$ 375$[/tex] \\
\hline
\end{tabular}

Collision & Comprehensive Premiums
\begin{tabular}{|c|c|c|}
\hline
Deductible & Collision & Comprehensive \\
\hline
\[tex]$ 100 & \$[/tex] 215 & \[tex]$ 129 \\
\hline
\$[/tex] 250 & \[tex]$ 185 & \$[/tex] 102 \\
\hline
\[tex]$ 500 & \$[/tex] 148 & \[tex]$ 85 \\
\hline
\end{tabular}

\ \textless \ strong\ \textgreater \ Rating Factor\ \textless \ /strong\ \textgreater \
\begin{tabular}{|c|c|c|}
\hline
Age & Male & Female \\
\hline
$[/tex]17-20[tex]$ & 2.30 & 1.45 \\
\hline
$[/tex]21-24[tex]$ & 2.15 & 1.2 \\
\hline
$[/tex]25-29$ & 1.55 & 1.0 \\
\hline
\end{tabular}



Answer :

To determine the total annual car insurance premium for a 21-year-old female driver who buys [tex]$25/50$[/tex] bodily injury liability insurance, [tex]$25$[/tex] property damage liability insurance, collision insurance with a [tex]$500 deductible, and comprehensive insurance with a $[/tex]250 deductible, we need to follow these steps:

Step 1: Determine the premiums for each type of insurance

1. Bodily Injury Liability Insurance:

- Coverage: [tex]$25/50$[/tex]
- Premium: \[tex]$220 2. Property Damage Liability Insurance: - Coverage: $[/tex]25[tex]$ - Premium: \$[/tex]175

3. Collision Insurance:

- Deductible: \[tex]$500 - Premium: \$[/tex]148

4. Comprehensive Insurance:

- Deductible: \[tex]$250 - Premium: \$[/tex]85

Step 2: Calculate the total liability insurance premium

Total Liability Premium:
[tex]\[ \text{Total Liability Premium} = \text{Bodily Injury Premium} + \text{Property Damage Premium} \][/tex]
[tex]\[ = \$220 + \$175 = \$395 \][/tex]

Step 3: Calculate the total collision and comprehensive insurance premiums

Total Collision and Comprehensive Premium:
[tex]\[ \text{Total Collision and Comprehensive Premium} = \text{Collision Premium} + \text{Comprehensive Premium} \][/tex]
[tex]\[ = \$148 + \$85 = \$233 \][/tex]

Step 4: Calculate the total cost without rating factor

Total Cost Without Rating Factor:
[tex]\[ \text{Total Cost} = \text{Total Liability Premium} + \text{Total Collision and Comprehensive Premium} \][/tex]
[tex]\[ = \$395 + \$233 = \$628 \][/tex]

Step 5: Apply the rating factor for a 21-year-old female

Rating Factor for a 21-year-old Female: [tex]\(1.2\)[/tex]

[tex]\[ \text{Total Premium} = \text{Total Cost} \times \text{Rating Factor} \][/tex]
[tex]\[ = \$628 \times 1.2 \][/tex]
[tex]\[ = \$753.6 \][/tex]

Conclusion:

The total annual car insurance premium for the 21-year-old female driver is:
[tex]\[ \boxed{\$753.6} \][/tex]