David is 22 years old. He buys 100/300/50 liability insurance, collision insurance with a \[tex]$100 deductible, and comprehensive insurance with a \$[/tex]500 deductible.

What is his total annual premium?

Liability Insurance
\begin{tabular}{|c|c|c|}
\hline
Type & Amount & Premium \\
\hline
\begin{tabular}{l}
Bodily \\
injury
\end{tabular} & 100/300 & \[tex]$310 \\
\hline
\begin{tabular}{c}
Property \\
damage
\end{tabular} & 50 & \$[/tex]50 \\
\hline
\end{tabular}

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

Rating Factor
\begin{tabular}{|c|c|c|}
\hline
Age & Male & Female \\
\hline
21-24 & 2.15 & 1.2 \\
\hline
\end{tabular}



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.