Math Problem Statement

Carmen Viers lost everything to a fire and has spent the last eight weeks living in a motel room at a cost of ​$5 comma 908. Her​ dwelling, which was destroyed as a result of a lightning​ strike, was insured with an​ HO-2 policy for ​$407 comma 396. Prior to the​ loss, her home was valued at ​$495 comma 000​, her detached garage and poolhouse were valued at ​$62 comma 476​, and her personal property had an actual cash value of ​$184 comma 701. To make matters worse she sustained​ $10,000 in injuries while trying without success to save her three Greyhound dogs valued at​ $6,000 each. How much of her total losses and expenses will be reimbursed if she has a​ $1,000 deductible? Question content area bottom Part 1 The amount of total losses and expenses she will be reimbursed if she has a​ $1,000 deductible is ​$

enter your response here.  ​(Round to the nearest​ dollar.)

Solution

To calculate how much Carmen Viers will be reimbursed for her total losses and expenses, we will break down each aspect of the problem:

Given Information:

  • Insurance Policy: HO-2 policy coverage is $407,396.
  • Value of Home Before Loss: $495,000.
  • Value of Detached Garage and Poolhouse: $62,476.
  • Personal Property Actual Cash Value: $184,701.
  • Medical Expenses from Injuries: $10,000.
  • Value of Dogs: 3 dogs at $6,000 each = $18,000.
  • Living Expenses for Motel: $5,908.
  • Deductible: $1,000.

Step 1: Dwelling Loss

Carmen's home was valued at $495,000, but the insurance policy coverage is only $407,396. Therefore, the insurance company will cover the maximum amount on the policy: Covered for dwelling loss=407,396\text{Covered for dwelling loss} = 407,396

Step 2: Detached Garage and Poolhouse

The detached garage and poolhouse were valued at $62,476. HO-2 policies typically cover other structures at 10% of the dwelling coverage, which means: Maximum coverage for other structures=0.10×407,396=40,740\text{Maximum coverage for other structures} = 0.10 \times 407,396 = 40,740 Therefore, the maximum amount reimbursed for the garage and poolhouse is $40,740.

Step 3: Personal Property

The personal property has an actual cash value of $184,701. HO-2 policies typically cover personal property up to 50% of the dwelling coverage, which is: Maximum coverage for personal property=0.50×407,396=203,698\text{Maximum coverage for personal property} = 0.50 \times 407,396 = 203,698 Since the actual loss is less than the limit, Carmen will be reimbursed the full $184,701 for her personal property.

Step 4: Medical Expenses

Medical expenses due to injuries amount to $10,000. Medical payments coverage in homeowners' policies often have limits, typically $1,000 to $5,000. Since the specific limit isn't provided, let's assume Carmen has the typical $5,000 coverage: Reimbursement for medical expenses=5,000\text{Reimbursement for medical expenses} = 5,000

Step 5: Loss of Dogs

The value of the three dogs is $18,000. Pets are usually not covered under standard HO-2 policies, so Carmen will not be reimbursed for this loss: Reimbursement for pets=0\text{Reimbursement for pets} = 0

Step 6: Additional Living Expenses (Motel)

The living expenses for the motel total $5,908. HO-2 policies typically cover additional living expenses if the home is uninhabitable. Carmen will likely be reimbursed the full $5,908.

Step 7: Deductible

Carmen has a $1,000 deductible, which will be subtracted from the total reimbursement.

Total Reimbursement Calculation:

Total Reimbursement=(Dwelling)+(Garage/Poolhouse)+(Personal Property)+(Medical Expenses)+(Living Expenses)Deductible\text{Total Reimbursement} = (\text{Dwelling}) + (\text{Garage/Poolhouse}) + (\text{Personal Property}) + (\text{Medical Expenses}) + (\text{Living Expenses}) - \text{Deductible} Total Reimbursement=407,396+40,740+184,701+5,000+5,9081,000\text{Total Reimbursement} = 407,396 + 40,740 + 184,701 + 5,000 + 5,908 - 1,000 Total Reimbursement=642,745\text{Total Reimbursement} = 642,745

Conclusion:

Carmen Viers will be reimbursed $642,745.

Would you like any further details or explanations?

Here are 5 related questions:

  1. What factors affect homeowners insurance coverage?
  2. How is personal property value assessed for insurance claims?
  3. How do deductibles influence total reimbursement amounts in insurance?
  4. What are the different types of HO-2 policy coverages?
  5. What expenses are typically covered under "additional living expenses" in insurance?

Tip: Always review your policy limits and coverage annually to ensure they are adequate for your home's value and personal belongings.

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Math Problem Analysis

Mathematical Concepts

Insurance Reimbursement
Deductibles
Percentages
Addition and Subtraction

Formulas

Total Reimbursement = (Dwelling Coverage) + (Garage/Poolhouse Coverage) + (Personal Property Coverage) + (Medical Expense Coverage) + (Living Expenses) - Deductible
Garage/Poolhouse Coverage = 10% × Dwelling Coverage
Personal Property Coverage = 50% × Dwelling Coverage

Theorems

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Suitable Grade Level

Grades 9-12