Answer :
To determine David's total annual premium for his car insurance, we need to follow several steps. Here’s the detailed breakdown:
1. Identify the Premiums for Each Type of Insurance:
- Liability Insurance: David selected the [tex]$100/300 policy which has a premium of $[/tex]310.
- Collision Insurance: David has chosen the plan with a [tex]$100 deductible, so his premium is $[/tex]215.
- Comprehensive Insurance: David has selected the plan with a [tex]$500 deductible, giving him a premium of $[/tex]85.
2. Calculate the Base Premium:
To find the base premium, we sum the premiums for liability, collision, and comprehensive insurance:
[tex]\[ \text{Base Premium} = \text{Liability Premium} + \text{Collision Premium} + \text{Comprehensive Premium} \][/tex]
[tex]\[ \text{Base Premium} = 310 + 215 + 85 = 610 \][/tex]
3. Apply the Rating Factor:
David's rating factor is 2.15 because he is a 22-year-old male. Using this factor, we calculate the total annual premium:
[tex]\[ \text{Total Annual Premium} = \text{Base Premium} \times \text{Rating Factor} \][/tex]
[tex]\[ \text{Total Annual Premium} = 610 \times 2.15 = 1311.5 \][/tex]
Thus, David’s total annual premium for his car insurance is $1311.50.
1. Identify the Premiums for Each Type of Insurance:
- Liability Insurance: David selected the [tex]$100/300 policy which has a premium of $[/tex]310.
- Collision Insurance: David has chosen the plan with a [tex]$100 deductible, so his premium is $[/tex]215.
- Comprehensive Insurance: David has selected the plan with a [tex]$500 deductible, giving him a premium of $[/tex]85.
2. Calculate the Base Premium:
To find the base premium, we sum the premiums for liability, collision, and comprehensive insurance:
[tex]\[ \text{Base Premium} = \text{Liability Premium} + \text{Collision Premium} + \text{Comprehensive Premium} \][/tex]
[tex]\[ \text{Base Premium} = 310 + 215 + 85 = 610 \][/tex]
3. Apply the Rating Factor:
David's rating factor is 2.15 because he is a 22-year-old male. Using this factor, we calculate the total annual premium:
[tex]\[ \text{Total Annual Premium} = \text{Base Premium} \times \text{Rating Factor} \][/tex]
[tex]\[ \text{Total Annual Premium} = 610 \times 2.15 = 1311.5 \][/tex]
Thus, David’s total annual premium for his car insurance is $1311.50.