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

What is her total annual car insurance premium?

Liability Insurance:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Type} & \text{Amount} & \text{Premium} \\
\hline
\multirow{3}{*}{\text{Bodily Injury}} & 25/30 & \$5 \times 20 \\
\cline{2-3}
& 50/100 & \$50 \\
\cline{2-3}
& 100/300 & \$150 \\
\hline
\multirow{3}{*}{\text{Property Damage}} & 25 & \$175 \\
\cline{2-3}
& 30 & \$245 \\
\cline{2-3}
& 100 & \$405 \\
\hline
\end{array}
\][/tex]

Collision and Comprehensive Premiums:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{Deductible} & \text{Collision} & \text{Comprehensive} \\
\hline
\$700 & \$215 & \$129 \\
\hline
\$250 & \$165 & \$102 \\
\hline
\$500 & \$143 & \$85 \\
\hline
\end{array}
\][/tex]



Answer :

To determine the total annual car insurance premium for the 21-year-old female driver, we need to calculate the premiums for all components of her insurance policy, which include liability insurance, collision insurance, and comprehensive insurance.

### Liability Insurance

Bodily Injury Insurance:
- Coverage: [tex]$25,000/$[/tex]50,000 per person injured
- Premium for [tex]$25,000/$[/tex]50,000 coverage is [tex]$5 \times 20 = 100$[/tex]
- Coverage: [tex]$50,000/$[/tex]100,000 per person injured
- Premium for [tex]$100,000/$[/tex]350,000 coverage is [tex]$150 Premiums for Bodily Injury: - $[/tex]5 \times 20[tex]$ = $[/tex]100
- [tex]$100,000/$[/tex]350,000[tex]$ Bodily Injury = $[/tex]150

Property Damage Insurance:
- Coverage: [tex]$25,000 - Premium for $[/tex]25,000 property damage coverage is [tex]$175 - Coverage: $[/tex]30,000
- Premium for [tex]$30,000 property damage coverage is $[/tex]245
- Coverage: [tex]$100,000 - Premium for $[/tex]100,000 property damage coverage is [tex]$75 Premiums for Property Damage: - $[/tex]25,000 Property Damage = [tex]$175 - $[/tex]30,000 Property Damage = [tex]$245 - $[/tex]100,000 Property Damage = [tex]$75 Calculating the Total Premium for Liability Insurance: - Total Premium for Bodily Injury Insurance = $[/tex]100 + [tex]$150 = $[/tex]250
- Total Premium for Property Damage Insurance = [tex]$175 + $[/tex]245 + [tex]$75 = $[/tex]495

Total Liability Insurance Premium = [tex]$250 + $[/tex]495 = [tex]$745 ### Collision Insurance - The driver chooses a deductible of $[/tex]500
- Premium for [tex]$500 deductible collision insurance is $[/tex]143

Total Collision Insurance Premium = [tex]$143 ### Comprehensive Insurance - The driver chooses a deductible of $[/tex]250
- Premium for [tex]$250 deductible comprehensive insurance is $[/tex]129

Total Comprehensive Insurance Premium = [tex]$129 ### Total Annual Car Insurance Premium To calculate the total annual car insurance premium, we add up the premiums for liability insurance, collision insurance, and comprehensive insurance: Total Annual Car Insurance Premium = Total Liability Insurance Premium + Total Collision Insurance Premium + Total Comprehensive Insurance Premium Total Annual Car Insurance Premium = $[/tex]745 + [tex]$143 + $[/tex]129 = [tex]$1017 Thus, the total annual car insurance premium for the driver is $[/tex]1017.