Answer :
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.
[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.