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Jerry is currently insured through AA Auto Insurance and wants to lower his auto insurance premium by at least [tex]$10 per month. His current plan includes:

- $[/tex]50,000/[tex]$100,000 limit for bodily injury
- $[/tex]100,000 limit for property damage
- [tex]$250 deductible for collision
- $[/tex]50 deductible for comprehensive

Which of the following adjustments would allow Jerry to meet his goal?

\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{ AA Auto Insurance } \\
\hline Type of Insurance Coverage & Coverage Limits & Annual Premiums \\
\hline \multirow[t]{3}{*}{ Bodily Injury } & \[tex]$25 / \$[/tex]50,000 & \[tex]$22.50 \\
\hline & \$[/tex]50 / 100,000 & \[tex]$31.75 \\
\hline & \$[/tex]100 / 300,000 & \[tex]$40.25 \\
\hline \multirow[t]{3}{*}{ Property Damage } & \$[/tex]25,000 & \[tex]$120.50 \\
\hline & \$[/tex]50,000 & \[tex]$144.75 \\
\hline & \$[/tex]100,000 & \[tex]$193.00 \\
\hline \multirow[t]{3}{*}{ Collision } & \$[/tex]100 deductible & \[tex]$520.00 \\
\hline & \$[/tex]250 deductible & \[tex]$415.25 \\
\hline & \$[/tex]500 deductible & \[tex]$275.75 \\
\hline Comprehensive & \$[/tex]50 deductible & \$110.25 \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
Alright class, let's carefully go through the steps to determine which adjustments Jerry can make to lower his auto insurance premium by at least [tex]$10 per month. Jerry's goal is to reduce his current monthly premium from $[/tex]\[tex]$ 750.25$[/tex] to at most [tex]$\$[/tex] 740.25[tex]$. We'll evaluate different coverage modifications to see if they help meet this goal. First, let's take a look at Jerry's current monthly premiums: - Bodily Injury ( \$[/tex]50 / 100,000): \[tex]$31.75 - Property Damage ( \$[/tex]100,000): \[tex]$193.00 - Collision ( \$[/tex]250 deductible): \[tex]$415.25 - Comprehensive ( \$[/tex]50 deductible): \[tex]$110.25 The current total monthly premium is calculated as: \[ 31.75 + 193.00 + 415.25 + 110.25 = 750.25 \] Jerry wants to lower this to at least \$[/tex]10 less:
[tex]\[ 750.25 - 10 = 740.25 \][/tex]

Now, let's evaluate each adjustment:

1. Lower Bodily Injury to \[tex]$25 / 50,000: - New Bodily Injury premium: \$[/tex]22.50
- New Total Premium:
[tex]\[ 22.50 + 193.00 + 415.25 + 110.25 = 741.00 \][/tex]
This change reduces the premium but does not meet the \[tex]$740.25 goal. 2. Lower Bodily Injury to \$[/tex]100 / 300,000:
- New Bodily Injury premium: \[tex]$40.25 - New Total Premium: \[ 40.25 + 193.00 + 415.25 + 110.25 = 758.75 \] This increase in bodily injury limit increases the premium, making it worse than the current premium. 3. Lower Property Damage to \$[/tex]50,000:
- New Property Damage premium: \[tex]$144.75 - New Total Premium: \[ 31.75 + 144.75 + 415.25 + 110.25 = 702.00 \] This change reduces the premium significantly below the goal. 4. Lower Property Damage to \$[/tex]25,000:
- New Property Damage premium: \[tex]$120.50 - New Total Premium: \[ 31.75 + 120.50 + 415.25 + 110.25 = 677.75 \] This change also significantly reduces the premium. 5. Increase Collision deductible to \$[/tex]500:
- New Collision premium: \[tex]$275.75 - New Total Premium: \[ 31.75 + 193.00 + 275.75 + 110.25 = 610.75 \] This change significantly reduces the premium as well. Next, let's determine the options that meet Jerry's goal of reducing the premium to at most \$[/tex]740.25. The valid options are those with new premiums less than or equal to \[tex]$740.25. The valid options from our analysis are: - Option 3: Lower Property Damage to \$[/tex]50,000
- Option 4: Lower Property Damage to \[tex]$25,000 - Option 5: Increase Collision deductible to \$[/tex]500

So, the possible options for Jerry to lower his premium by at least \$10 per month are:

Options 3, 4, and 5.
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