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]
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]