Calculate the monthly payment for an insurance plan including the following options:

- Bodily Injury: [tex]$50,000 / $[/tex]100,000
- Property Damage: [tex]$100,000
- Collision: $[/tex]500 deductible
- Comprehensive: [tex]$100 deductible

| Type of Insurance | Coverage Limits | Annual Premiums |
|-------------------|----------------------|-----------------|
| Bodily Injury | $[/tex]25 / [tex]$50,000 | $[/tex]22.50 |
| | [tex]$50 / $[/tex]100,000 | [tex]$31.75 |
| | $[/tex]100 / [tex]$300,000 | $[/tex]40.25 |
| Property Damage | [tex]$25,000 | $[/tex]120.50 |
| | [tex]$50,000 | $[/tex]144.75 |
| | [tex]$100,000 | $[/tex]193.00 |
| Collision | [tex]$100 deductible | $[/tex]520.00 |
| | [tex]$250 deductible | $[/tex]415.25 |
| | [tex]$500 deductible | $[/tex]275.75 |



Answer :

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.

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