To find Cindy's new annual premium including the discount, let's follow a detailed, step-by-step solution:
1. Calculate the Total Original Annual Premium:
To find the total cost of her original premiums, sum up the individual annual premiums:
[tex]\[
\text{Bodily Injury} = \$ 31.75
\][/tex]
[tex]\[
\text{Property Damage} = \$ 120.50
\][/tex]
[tex]\[
\text{Collision} = \$ 275.75
\][/tex]
[tex]\[
\text{Comprehensive} = \$ 100.00
\][/tex]
Add these amounts together for the total original annual premium:
[tex]\[
\text{Total Original Annual Premium} = \[tex]$ 31.75 + \$[/tex] 120.50 + \[tex]$ 275.75 + \$[/tex] 100.00 = \$ 528.00
\][/tex]
2. Calculate the Discount Amount:
Cindy is offered a discount of 4.5%. To find the amount of the discount, multiply the total original annual premium by the discount rate:
[tex]\[
\text{Discount Rate} = \frac{4.5}{100} = 0.045
\][/tex]
Calculate the discount amount:
[tex]\[
\text{Discount Amount} = \[tex]$ 528.00 \times 0.045 = \$[/tex] 23.76
\][/tex]
3. Calculate the New Annual Premium:
To find the new annual premium after applying the discount, subtract the discount amount from the total original annual premium:
[tex]\[
\text{New Annual Premium} = \[tex]$ 528.00 - \$[/tex] 23.76 = \$ 504.24
\][/tex]
Thus, Cindy's new annual premium, including the discount, is:
[tex]\[
\boxed{\$ 504.24}
\][/tex]
The correct answer is:
a. \$ 504.24
