Susie is thinking about changing her auto insurance policy at Fret-No-More Auto Insurance. Her current policy includes the following options: $50/100,000 limit for bodily injury, $25,000 limit for property damage, $250 deductible for collision, and $50 deductible for comprehensive. Which of the following changes would increase Susie’s limits the most without increasing her monthly premium by more than $5.00?

Question

Fret-No-More Auto Insurance
Type of Insurance Coverage
Coverage Limits
Annual Premiums
Bodily Injury
$25/50,000
$21.35

$50/100,000
$32.78

$100/300,000
$42.10

Property Damage
$25,000
$115.50

$50,000
$142.44

$100,000
$193.78

Collision
$100 deductible
$490.25

$250 deductible
$343.33

$500 deductible
$248.08

Comprehensive
$50 deductible
$105.79

$100 deductible
$88.23

a.
Increase coverage on bodily injury to $100/300,000.
b.
Increase coverage on property damage to $50,000.
c.
Increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.
d.
Increase coverage on bodily injury to $100/300,000 and on property damage to $100,000.

Answer 1

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:

1. Bodily Injury: $50/100,000 - $32.78 (annual)
2. Property Damage: $25,000 - $115.50 (annual)
3. Collision: $250 deductible - $343.33 (annual)
4. 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.