AAA Insurance has offered to insure their home for an annual premium of [tex]$0.38 per $[/tex]100 with a [tex]$500 deductible. Thompson's Insurance has offered to insure the same home for an annual premium of $[/tex]0.26 per [tex]$100 with a $[/tex]1,000 deductible.

| Insurance Company | Annual Premium (per [tex]$100) | Deductible |
|----------------------|---------------------------|------------|
| AAA Insurance | $[/tex]0.38 | [tex]$500 |
| Thompson's Insurance | $[/tex]0.26 | [tex]$1,000 |

The house Tara and Levi purchased is valued at $[/tex]425,000. Which of the following statements accurately describes the difference between the two plans?

a. AAA Insurance is cheapest if Tara and Levi experience an incident that results in severe damage or loss to their home.
b. AAA Insurance would be cheapest if Tara and Levi can avoid any incidents that result in severe damage or loss to their home.
c. Thompson's Insurance is cheaper even if Tara and Levi experience an incident that results in severe damage or loss to their home.
d. Thompson's will be more expensive whether or not Tara and Levi experience an incident.

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.