To calculate the monthly payment for an insurance plan including the specified options, we need to go through a few clear steps, ensuring we select the correct premiums for each type of coverage and then determine the total annual premium before converting it into a monthly payment.
### Step-by-Step Solution:
1. Identify the Annual Premiums for Each Type of Coverage:
- Bodily Injury:
The selected coverage is \[tex]$50 / 100,000, and according to the given table, the annual premium is \$[/tex]31.75.
- Property Damage:
The selected coverage is \[tex]$100,000, and the annual premium for this coverage is \$[/tex]193.00.
- Collision:
The selected deductible is \[tex]$500, and the annual premium for this deductible is \$[/tex]275.75.
- Comprehensive:
The selected deductible is \[tex]$100. According to the table, it's assumed that this comes without an additional cost, so the annual premium is \$[/tex]0.
2. Calculate the Total Annual Premium:
[tex]\[
\text{Total Annual Premium} = \text{Bodily Injury Annual} + \text{Property Damage Annual} + \text{Collision Annual} + \text{Comprehensive Annual}
\][/tex]
Substituting the values we've identified:
[tex]\[
\text{Total Annual Premium} = 31.75 + 193.00 + 275.75 + 0
\][/tex]
Adding these values together:
[tex]\[
\text{Total Annual Premium} = 500.50
\][/tex]
3. Convert the Total Annual Premium to a Monthly Payment:
To find the monthly payment, we divide the total annual premium by 12 (since there are 12 months in a year):
[tex]\[
\text{Monthly Payment} = \frac{\text{Total Annual Premium}}{12}
\][/tex]
Substituting the total annual premium:
[tex]\[
\text{Monthly Payment} = \frac{500.50}{12}
\][/tex]
Performing the division:
[tex]\[
\text{Monthly Payment} \approx 41.71
\][/tex]
Therefore, the total annual premium is \[tex]$500.50 and the monthly payment for the insurance plan is approximately \$[/tex]41.71.
