After reviewing her driving record for the past 3 years, Cindy's insurance company offers her a good driver discount of [tex]$4.5 \%$[/tex]. Her original policy was based on the premiums listed below. What is her new annual premium including the discount?

\begin{tabular}{|l|c|c|}
\hline
\multicolumn{3}{|c|}{Cindy's Auto Insurance Policy} \\
\hline
Type of Insurance Coverage & Coverage Limits & Annual Premiums \\
\hline
Bodily Injury & [tex]$\$[/tex] 50 / 100,000[tex]$ & $[/tex]\[tex]$ 31.75$[/tex] \\
\hline
Property Damage & [tex]$\$[/tex] 25,000[tex]$ & $[/tex]\[tex]$ 120.50$[/tex] \\
\hline
Collision & [tex]$\$[/tex] 500[tex]$ deductible & $[/tex]\[tex]$ 275.75$[/tex] \\
\hline
Comprehensive & [tex]$\$[/tex] 100[tex]$ deductible & $[/tex]\[tex]$ 100.00$[/tex] \\
\hline
\end{tabular}

a. [tex]$\$[/tex] 504.24[tex]$
b. $[/tex]\[tex]$ 523.50$[/tex]
c. [tex]$\$[/tex] 528.00[tex]$
d. $[/tex]\[tex]$ 551.76$[/tex]



Answer :

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]$\$[/tex]504.24$