To determine Cindy's new annual premium after a good driver discount, let's follow these steps:
1. Calculate the total original annual premium:
We need to add up all the annual premiums for each type of insurance coverage.
[tex]\[
\text{Total original premium} = \$31.75 (\text{Bodily Injury}) + \$120.50 (\text{Property Damage}) + \$275.75 (\text{Collision}) + \$100.00 (\text{Comprehensive})
\][/tex]
Adding these values together:
[tex]\[
\text{Total original premium} = \$31.75 + \$120.50 + \$275.75 + \$100.00 = \$528.00
\][/tex]
2. Calculate the discount amount:
The discount rate provided is [tex]\(4.5\%\)[/tex]. To find the discount amount, we multiply the total original premium by the discount rate:
[tex]\[
\text{Discount amount} = \$528.00 \times \left(\frac{4.5}{100}\right) = \$528.00 \times 0.045 = \$23.76
\][/tex]
3. Calculate the new annual premium after the discount:
To find the new annual premium, we subtract the discount amount from the total original premium:
[tex]\[
\text{New annual premium} = \$528.00 - \$23.76 = \$504.24
\][/tex]
Therefore, Cindy's new annual premium, after applying the good driver discount, is:
[tex]\[
\boxed{\$504.24}
\][/tex]
So, the correct answer is:
a. [tex]$\$[/tex]504.24$
