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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?



\multicolumn{3}{|c|}{Fret-No-More Auto Insurance}

Type of Insurance Coverage		Coverage LimitsAnnual 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

Verified Answer :

  • Calculate the annual budget limit: \(\$5.00 \times 12 = \$60.00\).
  • Analyze premium increases for available upgrades:
  • Bodily Injury (\$100/300k): \(\$9.32\) (Valid)
  • Property Damage (\$50k): \(\$26.94\) (Valid)
  • Property Damage (\$100k): \(\$78.28\) (Invalid)
  • Collision (\$100 deductible): \(\$146.92\) (Invalid)
  • Select the most significant valid upgrade: \(\boxed{\text{Property Damage to \$50,000}}\)

Explanation

  1. Analysis of Current Policy and Constraints

Susie's current insurance policy has the following annual premiums for her coverage:

  • Bodily Injury (\$50/100,000): \(\$32.78\)
  • Property Damage (\$25,000): \(\$115.50\)
  • Collision (\$250 deductible): \(\$343.33\)

Susie wants to increase her coverage limits without increasing her monthly premium by more than \(\$5.00\). This monthly limit corresponds to an annual premium increase cap of:
\[\$5.00 \times 12 \text{ months} = \$60.00 \text{ per year.}\]

  1. Evaluating Potential Upgrades

We evaluate each potential upgrade to her policy to determine the annual cost increase and check if it satisfies the \(\$60.00\) limit:

  1. Bodily Injury Upgrade (to \$100/300,000):
  • Increase in cost: \(\$42.10 - \$32.78 = \$9.32\) per year. (Valid)
  1. Property Damage Upgrade (to \$50,000):
  • Increase in cost: \(\$142.44 - \$115.50 = \$26.94\) per year. (Valid)
  1. Property Damage Upgrade (to \$100,000):
  • Increase in cost: \(\$193.78 - \$115.50 = \$78.28\) per year. (Exceeds \(\$60.00\) limit, so invalid.)
  1. Collision Upgrade (to \$100 deductible):
  • Increase in cost: \(\$490.25 - \$343.33 = \$146.92\) per year. (Exceeds \(\$60.00\) limit, so invalid.)
  1. Determining the Greatest Increase in Limits

We have two valid options that increase her coverage:

  • Upgrading Bodily Injury to \$100/300,000 increases the limit by a factor of 2 on the first value and 3 on the second.
  • Upgrading Property Damage to \$50,000 doubles her coverage from \$25,000 to \$50,000.

Comparing the "amount" of increase, the upgrade from \$25,000 to \$50,000 in Property Damage is a substantial doubling of her protection limit for that category. While both are valid, upgrading Property Damage to \$50,000 represents a significant adjustment in her coverage within the allowed budget. However, looking at the Bodily Injury limits, moving from \$50/100k to \$100/300k offers a broader protection expansion across both individual and per-accident claims. Between these, the Property Damage upgrade to \$50,000 is a clear, single-tier increase in coverage limits.

  1. Conclusion

Based on the analysis, the upgrade to Property Damage (\$50,000 limit) is the most significant increase in coverage that remains within the allowed budget. The final answer is the change to a \(\$50,000\) limit for property damage.

\(\boxed{\text{Property Damage to \$50,000}}\)

Examples

In insurance, maximizing coverage while balancing costs is a common financial puzzle. Similar to how you evaluate policy changes, you might calculate the benefit-to-cost ratio for other subscriptions, such as upgrading a streaming service, data plan, or professional membership, to ensure you get the best value without overstretching your monthly budget. Applying these calculations allows for informed decisions that protect your assets efficiently.

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