To determine Cindy's new annual premium including the good driver discount, let's go through the step-by-step calculation:
1. Calculate the total original premium costs:
- Bodily Injury premium: \[tex]$31.75
- Property Damage premium: \$[/tex]120.50
- Collision premium: \[tex]$275.75
- Comprehensive premium: \$[/tex]100.00
Adding these amounts together:
[tex]\[
\text{Total Premium} = 31.75 + 120.50 + 275.75 + 100.00 = 528.00
\][/tex]
2. Determine the discount amount:
- The discount rate is 4.5%, or 0.045 in decimal form.
Calculate the discount amount by multiplying the total premium by the discount rate:
[tex]\[
\text{Discount Amount} = 528.00 \times 0.045 = 23.76
\][/tex]
3. Calculate the new premium after applying the discount:
Subtract the discount amount from the total premium:
[tex]\[
\text{New Premium} = 528.00 - 23.76 = 504.24
\][/tex]
Thus, Cindy's new annual premium after applying the discount is:
[tex]\[
\boxed{504.24}
\][/tex]
So, the correct answer is:
a. [tex]$\$[/tex]504.24$
