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: $$597.40+42.10-32.78=606.72\text{ (annual)}\to \frac{606.72}{12}\approx 50.56\text{ (monthly)}$$ 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: $$597.40+142.44-115.50=624.34\text{ (annual)}\to \frac{624.34}{12}\approx 52.03\text{ (monthly)}$$ 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: $$597.40+42.10+142.44-32.78-115.50=633.66\text{ (annual)}\to \frac{633.66}{12}\approx 52.80\text{ (monthly)}$$ 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: $$597.40+42.10+193.78-32.78-115.50=686.78\text{ (annual)}\to \frac{686.78}{12}\approx 57.23\text{ (monthly)}$$

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.