To determine which option increases Susie’s limits the most without exceeding a $5.00 increase in her monthly premium, we first need to establish what her current annual premium is and how it compares to the options available.
Current Policy:
- Bodily Injury: $50/100,000 - $32.78 (annual)
- Property Damage: $25,000 - $115.50 (annual)
- Collision: $250 deductible - $343.33 (annual)
- Comprehensive: $50 deductible - $105.79 (annual)
Current Total Annual Premium:
- Bodily Injury: $32.78
- Property Damage: $115.50
- Collision: $343.33
- Comprehensive: $105.79
Calculating the total: \[ 32.78 + 115.50 + 343.33 + 105.79 = 597.40 \text{ (annual)} \]
Current Monthly Premium: \[ \frac{597.40}{12} \approx 49.78 \]
Adding $5 results in: \[ 49.78 + 5 = 54.78 \text{ (monthly)} \]
Available Options:
Next, we’ll evaluate each option against the allowed increased monthly premium of $54.78.
a. Increase coverage on bodily injury to $100/300,000.
- New Premium: $42.10 (annual)
- Change: $42.10 - $32.78 = $9.32 (annual)
New Total Premium: \[ 597.40 + 42.10 - 32.78 = 606.72 \text{ (annual)} \rightarrow \frac{606.72}{12} \approx 50.56 \text{ (monthly)} \] Increase in coverage: \(100,000\) increase in bodily injury from \(50,000\) limit to \(300,000\).
b. Increase coverage on property damage to $50,000.
- New Premium: $142.44 (annual)
- Change: $142.44 - $115.50 = $26.94 (annual)
New Total Premium: \[ 597.40 + 142.44 - 115.50 = 624.34 \text{ (annual)} \rightarrow \frac{624.34}{12} \approx 52.03 \text{ (monthly)} \] Increase in coverage: \(25,000\) increase in property damage (from $25,000 to $50,000).
c. Increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.
- New Premium Total:
- Bodily Injury: $42.10 (annual)
- Property Damage: $142.44 (annual)
Sum of changes: Change in Bodily Injury: $42.10 - $32.78 = $9.32 (annual) Change in Property Damage: $142.44 - $115.50 = $26.94 (annual) Total change = $9.32 + $26.94 = $36.26 (annual)
New Total Premium: \[ 597.40 + 42.10 + 142.44 - 32.78 - 115.50 = 633.66 \text{ (annual)} \rightarrow \frac{633.66}{12} \approx 52.80 \text{ (monthly)} \] Increase in coverage: \(100,000\) increase in bodily injury up to \(300,000\) + \(25,000\) in property damage.
d. Increase coverage on bodily injury to $100/300,000 and on property damage to $100,000.
- New Premiums:
- Bodily Injury: $42.10 (annual)
- Property Damage: $193.78 (annual)
Sum of changes: Change: (9.32 + 78.28= 36.26 + 78.28 Total: $65.72 (annual)
New Total Premium: \[ 597.40 + 42.10 + 193.78 - 32.78 - 115.50 = 686.78 \text{ (annual)} \rightarrow \frac{686.78}{12} \approx 57.23 \text{ (monthly)} \]
Summary of Increases:
- a: +$100,000 bodily injury, $50.56.
- b: +$25,000 property damage, $52.03.
- c: +$100,000 body, +$25,000 property damage, $52.80.
- d: +$100,000 body, +$75,000 property damage, $57.23.
Best Option: Option b - Increase coverage on property damage to $50,000 gives the most increase without exceeding the $5.00 increase in the monthly premium.
Select: b. Increase coverage on property damage to $50,000.