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Calculate the insurance costs.

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
\multicolumn{7}{|l|}{\begin{tabular}{l}
\begin{tabular}{|l|l|l|l|l|}
\hline
Bodily Injury & & & & \\
(in [tex]$\$[/tex] 1,000^{\prime}[tex]$ s): & & & & \\
\hline
\end{tabular}
\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}{|l|}{ 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 Descriptions:

- 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.

Questions:

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

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

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

Sagot :

GinnyAnsweridn
Certainly, let's tackle this step-by-step:

### a. Premium for a twenty-one-year-old single man who owns his car, purchasing insurance in the amount of 50/100/10
Given:
- Class: 2B (Unmarried male driver under 25 who is owner of the car)
- Bodily Injury Coverage: [tex]$50,000 / $[/tex]100,000[tex]$ - Property Damage Coverage: $[/tex]10,000[tex]$ From the table provided: - Bodily Injury for 50/100: $[/tex](Class\,2B)[tex]$ $[/tex]917.90
- Property Damage for \[tex]$10,000: $[/tex](Class\,2B)[tex]$ $[/tex]180.00

To find the total cost, we add the bodily injury coverage and the property damage coverage:
[tex]\[ 917.90 (Bodily Injury) + 180.00 (Property Damage) \][/tex]

So, the total cost for insurance in the amount of [tex]$50,000 / $[/tex]100,000[tex]$ bodily injury and $[/tex]10,000[tex]$ property damage is: \[ 1097.90 \] ### b. Cost to purchase insurance in the amount of 100/300/25 Given: - Class: 2B (Unmarried male driver under 25 who is owner of the car) - Bodily Injury Coverage: $[/tex]100,000 / [tex]$300,000$[/tex]
- Property Damage Coverage: [tex]$25,000$[/tex]

From the table provided:
- Bodily Injury for 100/300: [tex]$(Class\,2B)$[/tex] [tex]$976.96 - Property Damage for \$[/tex]25,000: [tex]$(Class\,2B)$[/tex] [tex]$196.60 To find the total cost, we add the bodily injury coverage and the property damage coverage: \[ 976.96 (Bodily Injury) + 196.60 (Property Damage) \] So, the total cost for insurance in the amount of $[/tex]100,000 / [tex]$300,000$[/tex] bodily injury and [tex]$25,000$[/tex] property damage is:
[tex]\[ 1173.56 \][/tex]

### c. Difference in cost
The difference in cost is obtained by subtracting the cost of the lower coverage from the higher coverage:
[tex]\[ 1173.56 - 1097.90 \][/tex]

So, the difference in cost for upgrading the insurance policy from 50/100/10 to 100/300/25 is:
[tex]\[ 75.66 \][/tex]

### Summary
a. The premium for a twenty-one-year-old single man who owns his car, purchasing insurance in the amount of 50/100/10 is [tex]$1097.90 b. The cost to purchase insurance in the amount of $[/tex]100/300/25 is [tex]$1173.56 c. The difference in cost between the two insurance coverages is $[/tex]75.66
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