Let's analyze the insurance plans for Tara and Levi's home, which is valued at \[tex]$425,000.
### AAA Insurance
1. Annual Premium Calculation:
\[
0.38 \text{ per } 100 \text{ } \text{\$[/tex]}
\]
For a house worth \[tex]$425,000:
\[
\text{Annual premium} = \left( \frac{425,000}{100} \right) \times 0.38 = 4250 \times 0.38 = 1615 \text{ } \text{\$[/tex]}
\]
2. Deductible:
[tex]\[
500 \text{ } \text{\$}
\][/tex]
3. Total Cost in Case of Severe Damage or Loss:
[tex]\[
\text{Total cost} = \text{Annual Premium} + \text{Deductible} = 1615 + 500 = 2115 \text{ } \text{\$}
\][/tex]
### Thompson's Insurance
1. Annual Premium Calculation:
[tex]\[
0.26 \text{ per } 100 \text{ } \text{\$}
\][/tex]
For a house worth \[tex]$425,000:
\[
\text{Annual premium} = \left( \frac{425,000}{100} \right) \times 0.26 = 4250 \times 0.26 = 1105 \text{ } \text{\$[/tex]}
\]
2. Deductible:
[tex]\[
1000 \text{ } \text{\$}
\][/tex]
3. Total Cost in Case of Severe Damage or Loss:
[tex]\[
\text{Total cost} = \text{Annual Premium} + \text{Deductible} = 1105 + 1000 = 2105 \text{ } \text{\$}
\][/tex]
### Comparison of the Plans:
- Annual Premium:
- AAA Insurance: 1615 \[tex]$
- Thompson's Insurance: 1105 \$[/tex]
Thompson's Insurance has a lower annual premium.
- Total Cost in Case of Severe Damage or Loss:
- AAA Insurance: 2115 \[tex]$
- Thompson's Insurance: 2105 \$[/tex]
Thompson's Insurance has a lower total cost even in the event of severe damage or loss.
Therefore, the statement that accurately describes the difference between the two plans is:
c. Thompson's Insurance is cheaper even if Tara and Levi experience an incident that results in severe damage or loss to their home.
