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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]$50,000/\$[/tex]100,000 & \[tex]$31.75 \\
\hline
Property Damage & \$[/tex]25,000 & \[tex]$120.50 \\
\hline
Collision & \$[/tex]500 deductible & \[tex]$275.75 \\
\hline
Comprehensive & \$[/tex]100 deductible & \[tex]$100.00 \\
\hline
\end{tabular}

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



Answer :

GinnyAnswer
Let's determine Cindy's new annual premium after applying the good driver discount by going through a detailed, step-by-step solution.

1. Calculate the total original annual premium:
First, add up all the individual premiums for each type of insurance coverage:
- Bodily Injury Premium: \[tex]$31.75 - Property Damage Premium: \$[/tex]120.50
- Collision Premium: \[tex]$275.75 - Comprehensive Premium: \$[/tex]100.00

[tex]\[ \text{Total Original Annual Premium} = 31.75 + 120.50 + 275.75 + 100.00 = 528.00 \text{ dollars} \][/tex]

2. Calculate the discount amount:
Cindy is offered a discount of 4.5%. To find the discount amount, we need to calculate 4.5% of the total original annual premium.

[tex]\[ \text{Discount Amount} = \left( \frac{4.5}{100} \right) \times 528.00 = \frac{4.5}{100} \times 528.00 = 23.76 \text{ dollars} \][/tex]

3. Calculate the new annual premium including the discount:
Subtract the discount amount from the total original annual premium to find the new annual premium.

[tex]\[ \text{New Annual Premium} = 528.00 - 23.76 = 504.24 \text{ dollars} \][/tex]

Therefore, Cindy's new annual premium including the discount is:

a. \$504.24

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