AUTOMOBILE LIABILITY BASIC INSURANCE PREMIUMS

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline Coverage & Class 1A & Class 1B & Class 1C & Class 2A & Class 2B & Class 3 \\
\hline \begin{tabular}{l}
Bodily Injury \\
(in [tex]$\$[/tex] 1,000^{\prime}[tex]$ ):
\end{tabular} & & & & & & \\
\hline $[/tex]10 / 20[tex]$ & 317.80 & 365.40 & 413.40 & 587.00 & 761.00 & 428.40 \\
\hline $[/tex]50 / 100[tex]$ & 383.60 & 440.70 & 497.80 & 709.30 & 917.90 & 517.60 \\
\hline $[/tex]100 / 300[tex]$ & 407.50 & 469.90 & 530.92 & 751.88 & 976.96 & 549.70 \\
\hline \multicolumn{7}{|c|}{ Property Damage: } \\
\hline$[/tex]\[tex]$ 5,000$[/tex] & 61.00 & 69.40 & 79.80 & 113.40 & 163.80 & 81.80 \\
\hline[tex]$\$[/tex] 10,000[tex]$ & 67.00 & 76.20 & 87.80 & 124.80 & 180.00 & 90.00 \\
\hline$[/tex]\[tex]$ 25,000$[/tex] & 73.20 & 84.80 & 96.80 & 136.00 & 196.60 & 98.20 \\
\hline
\end{tabular}

Class 1A: No male driver under 25; car not used for business and not driven to or from work.
Class 1B: No male driver under 25; car not used for business and driven to work fewer than ten miles away.
Class 1C: No male driver under 25; car not used for business and driven to work at least ten miles away.
Class 2A: One or more male drivers under 25 who are married or are not owner(s) of the car.
Class 2B: Unmarried male driver under 25 who is owner of the car.
Class 3: No male driver under 25; car used for business.

a. What would be the premium for a twenty-one-year-old single man who owns his car, purchasing insurance in the amount of [tex]$50 / 100 / 10$[/tex]?

b. How much would it cost him to purchase insurance in the amount of [tex]$100 / 300 / 25$[/tex]?

c. What is the difference in cost? [tex]$\square$[/tex]

Certainly! Let's walk through the problem step-by-step:

### Situation Overview
We have a twenty-one-year-old single man who owns his car. According to the problem, he falls into "Class 2B."

### Objective
We want to determine:
a. The premium for purchasing insurance with coverage amounts of \[tex]$50,000/$[/tex]100,000 Bodily Injury and [tex]$10,000 Property Damage. b. The premium for the same person with coverage amounts of \$[/tex]100,000/[tex]$300,000 Bodily Injury and $[/tex]25,000 Property Damage.
c. The difference in cost between the two premium amounts.

### Solution

#### a. Premium for [tex]$50/100$[/tex] Bodily Injury and [tex]$10,000 Property Damage 1. Bodily Injury Coverage: - From the table, for "Class 2B" and coverage of $[/tex]50,000/[tex]$100,000, the premium is $[/tex]917.90.

2. Property Damage Coverage:
- From the table, for "Class 2B" and coverage of [tex]$10,000, the premium is $[/tex]90.00.

3. Total Premium:
- Adding these two premiums together:
[tex]\[ 917.90 + 90.00 = 1007.90 \][/tex]

So, the total premium for a twenty-one-year-old single man who owns his car and purchases insurance with [tex]$50,000/$[/tex]100,000 Bodily Injury and [tex]$10,000 Property Damage is $[/tex]1007.90.

#### b. Premium for [tex]$100/300$[/tex] Bodily Injury and [tex]$25,000 Property Damage 1. Bodily Injury Coverage: - From the table, for "Class 2B" and coverage of $[/tex]100,000/[tex]$300,000, the premium is $[/tex]976.96.

2. Property Damage Coverage:
- From the table, for "Class 2B" and coverage of [tex]$25,000, the premium is $[/tex]98.20.

3. Total Premium:
- Adding these two premiums together:
[tex]\[ 976.96 + 98.20 = 1075.16 \][/tex]

So, the total premium for the same person purchasing insurance with [tex]$100,000/$[/tex]300,000 Bodily Injury and [tex]$25,000 Property Damage is $[/tex]1075.16.

#### c. Difference in Cost

1. Premium for [tex]$50/100/10: - As calculated in part (a), the premium is $[/tex]1007.90.

2. Premium for [tex]$100/300/25: - As calculated in part (b), the premium is $[/tex]1075.16.

3. Difference in Cost:
- Subtract the lesser premium from the greater premium:
[tex]\[ 1075.16 - 1007.90 = 67.26 \][/tex]

So, the difference in cost between purchasing insurance with [tex]$100,000/$[/tex]300,000 Bodily Injury and [tex]$25,000 Property Damage versus $[/tex]50,000/[tex]$100,000 Bodily Injury and $[/tex]10,000 Property Damage is [tex]$67.26. ### Summary - Premium for $[/tex]50/100/10: [tex]$1007.90 - Premium for $[/tex]100/300/25: [tex]$1075.16 - Difference in Cost: $[/tex]67.26