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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{2}{|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]\$504.24[/tex]

b. [tex]\$523.50[/tex]

c. [tex]\$528.00[/tex]

d. [tex]\$551.76[/tex]



Answer :

GinnyAnswer
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]$\$[/tex]504.24$

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