Answer :
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
### 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