Answered

The table below lists the insurance options offered by AA Auto Insurance. Calculate the monthly payment for an insurance plan including the following options:



Bodily Injury: \$50/100,000

Property Damage: \$100,000

Collision: \$500 deductible

Comprehensive: \$100 deductible



\multicolumn{3}{|c|}{AA Auto Insurance}

Type of Insurance Coverage		Coverage LimitsAnnual Premiums

Bodily Injury		\$25/\$50,000\$22.50

\$50/100,000\$31.75

\$100/300,000\$40.25


Property Damage		\$25,000\$120.50

\$50,000\$144.75

\$100,000\$193.00

Verified Answer :

  • Retrieve the annual premium for 'Bodily Injury' (\$50/100,000) as \$31.75.
  • Retrieve the annual premium for 'Property Damage' (\$100,000) as \$193.00.
  • Calculate the total annual premium: \(\$31.75 + \$193.00 = \$224.75\).
  • Divide by 12 to get the monthly payment: \(\frac{\$224.75}{12} \approx \boxed{\$18.73}\) (note that 'Collision' and 'Comprehensive' costs are missing).

Explanation

  1. Problem Analysis and Data Retrieval

We are asked to calculate the total monthly insurance premium for a policy with specific coverage limits. The coverage details are:

  1. Bodily Injury: \(\$50/100,000\)
  2. Property Damage: \(\$100,000\)
  3. Collision: \(\$500\) deductible
  4. Comprehensive: \(\$100\) deductible

We need to retrieve the annual premiums from the provided insurance table for these categories. Note that the table only lists premiums for 'Bodily Injury' and 'Property Damage'. There is no information provided regarding costs for 'Collision' or 'Comprehensive' coverage. Therefore, we will calculate the premium for the items available and indicate the missing data.

  1. Calculating Total Annual Premium

From the provided table:

  1. For Bodily Injury at the \(\$50/100,000\) coverage limit, the annual premium is \(\$31.75\).
  2. For Property Damage at the \(\$100,000\) coverage limit, the annual premium is \(\$193.00\).
  3. The annual premiums for 'Collision' and 'Comprehensive' coverage are not listed in the table, so they cannot be included in the calculation.

The total annual premium for the available coverage is the sum of these two amounts:
\[\text{Total Annual Premium} = \$31.75 + \$193.00 = \$224.75.\]

  1. Calculating Monthly Payment and Conclusion

To find the monthly payment, we divide the total annual premium by 12 months.
\[\text{Monthly Payment} = \frac{\$224.75}{12} \approx \$18.729166...\].
Rounding to the nearest cent, the monthly payment for the known portions of the plan is \(\$18.73\). Since the costs for 'Collision' and 'Comprehensive' are missing, the actual total monthly payment will be higher once these costs are included. The final answer for the available data is \(\boxed{\$18.73}\) per month, plus the cost of the collision and comprehensive coverage.

Examples

This problem illustrates how insurance companies structure costs based on coverage levels. Understanding how to interpret premium tables helps individuals estimate their monthly expenses. By knowing the annual costs and dividing by 12, consumers can effectively budget for recurring payments like insurance, taxes, or annual subscriptions. Always ensure you have all relevant cost information before calculating total commitments.