To determine Cindy's new annual premium including the 4.5% discount, we need to follow a step-by-step approach:
1. Calculate the total original annual premium:
We add up all the annual premiums for each type of coverage:
[tex]\[
\text{Total Original Annual Premium} = \$31.75 + \$120.50 + \$275.75 + \$100.00 = \$528.00
\][/tex]
2. Calculate the discount amount:
We know that Cindy is offered a discount of 4.5%. To find the discount amount, we need to apply this rate to the total original annual premium:
[tex]\[
\text{Discount Amount} = \text{Total Original Annual Premium} \times 0.045 = \$528.00 \times 0.045 = \$23.76
\][/tex]
3. Calculate the new annual premium after the discount:
Subtract the discount amount from the total original annual premium to get the new annual premium:
[tex]\[
\text{New Annual Premium} = \$528.00 - \$23.76 = \$504.24
\][/tex]
Therefore, Cindy's new annual premium including the 4.5% discount is [tex]$\$[/tex]504.24$.
The correct answer is:
[tex]\[
\boxed{504.24}
\][/tex]
