Let's determine Cindy's new annual premium after applying the good driver discount by going through a detailed, step-by-step solution.
1. Calculate the total original annual premium:
First, add up all the individual premiums for each type of insurance coverage:
- Bodily Injury Premium: \[tex]$31.75
- Property Damage Premium: \$[/tex]120.50
- Collision Premium: \[tex]$275.75
- Comprehensive Premium: \$[/tex]100.00
[tex]\[
\text{Total Original Annual Premium} = 31.75 + 120.50 + 275.75 + 100.00 = 528.00 \text{ dollars}
\][/tex]
2. Calculate the discount amount:
Cindy is offered a discount of 4.5%. To find the discount amount, we need to calculate 4.5% of the total original annual premium.
[tex]\[
\text{Discount Amount} = \left( \frac{4.5}{100} \right) \times 528.00 = \frac{4.5}{100} \times 528.00 = 23.76 \text{ dollars}
\][/tex]
3. Calculate the new annual premium including the discount:
Subtract the discount amount from the total original annual premium to find the new annual premium.
[tex]\[
\text{New Annual Premium} = 528.00 - 23.76 = 504.24 \text{ dollars}
\][/tex]
Therefore, Cindy's new annual premium including the discount is:
a. \$504.24
