Math Problem Statement

Sufficient Dwelling Coverage?

Colton Gentry of Lancaster, California, has owned his home for ten years. When he purchased it for $178,000, Colton bought a $160,000 homeowner's insurance policy. He still owns that policy, even though the replacement cost of the home is now $302,000.

If Colton suffered a $18,000 fire loss to the home, what percentage of the loss would be covered by his policy? Round your answer to one decimal place.

%

What dollar amount of the loss would be covered by his policy? Enter the amount of the loss as a positive number. Round your answer to the nearest dollar.

$

How much insurance on the home should Colton carry now to be fully reimbursed for a fire loss? Round your answer to the nearest dollar.

$

Solution

To solve these questions, we need to apply the "co-insurance" principle used in homeowners' insurance policies. This principle calculates the percentage of the loss covered based on the ratio of the insurance policy's coverage to the replacement cost of the home.

1. Percentage of the loss covered by the policy:

The formula to calculate the percentage of the loss covered is:

Percentage Covered=(Insurance Policy AmountReplacement Cost)×100\text{Percentage Covered} = \left( \frac{\text{Insurance Policy Amount}}{\text{Replacement Cost}} \right) \times 100

Substitute the values:

Percentage Covered=(160,000302,000)×10053.0%\text{Percentage Covered} = \left( \frac{160,000}{302,000} \right) \times 100 \approx 53.0\%

So, 53.0% of the fire loss would be covered by his policy.

2. Dollar amount of the loss covered:

To find the dollar amount covered, multiply the percentage of the loss covered by the total loss amount:

Amount Covered=(160,000302,000)×18,000\text{Amount Covered} = \left( \frac{160,000}{302,000} \right) \times 18,000

Amount Covered=0.530×18,000=9,540\text{Amount Covered} = 0.530 \times 18,000 = 9,540

So, the dollar amount of the loss covered by his policy is $9,540.

3. Amount of insurance Colton should carry:

To be fully reimbursed for any future loss, Colton should carry an insurance policy equal to the full replacement cost of his home, which is now $302,000.

Final Answers:

  • Percentage of the loss covered by the policy: 53.0%
  • Dollar amount of the loss covered by the policy: $9,540
  • Amount of insurance Colton should carry: $302,000

Would you like more details on how these calculations were made? Here are five related questions:

  1. What happens if Colton's replacement cost increases further?
  2. How does co-insurance affect smaller claims?
  3. What are the benefits of increasing insurance coverage over time?
  4. How does policy coverage differ between partial and total loss scenarios?
  5. How do insurance companies determine replacement costs?

Tip: It's a good idea to periodically review your homeowners' insurance to ensure that your coverage reflects your home's current replacement cost.

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Math Problem Analysis

Mathematical Concepts

Ratio
Percentage
Insurance Co-insurance

Formulas

Percentage Covered = (Insurance Policy Amount / Replacement Cost) * 100
Amount Covered = (Insurance Policy Amount / Replacement Cost) * Loss Amount

Theorems

Co-insurance principle in insurance policies

Suitable Grade Level

Grades 9-12