Question

. Math The Bowman Co. is considering self-insuring its vehicles

rather than purchasing an insurance policy. It examined three years
of losses and listed the costs of vehicle repairs for the three years.
a. What is the minimum and maximum annual cost of repairs?
b. What is the average annual cost of repairs for the three years?
c. If the company wants a one-year balance in the self-insurance
account that is 10 percent higher than the highest annual cost
of repairs, how much should it save each month?
Year 1
Year 2
Year 3
$3,584
$2,505
$450
$1,215
$13,582
$4,267
$794
$1,035
$6,024
$5,820
$1,995

Answer 1

For the Bowman Co. vehicle repairs over three years, the minimum annual cost of repairs is $10,291 and the maximum is $19,297. The average annual cost is $13,412. To have a self-insurance reserve 10% higher than the maximum cost, they should save $1,768.90 per month.

Step-by-step explanation:

To answer the student's question regarding the Bowman Co. and their consideration of self-insuring their vehicles, given the data for three years, we can proceed as follows:

• a. To find the minimum and maximum annual cost of repairs, we look at the costs provided for each year. For Year 1, the total cost is $3,584 + $450 + $794 + $5,820 = $10,648. Year 2 is $2,505 + $1,215 + $13,582 + $1,995 = $19,297. Year 3 is $4,267 + $6,024 for a total of $10,291. Therefore, the minimum cost is $10,291 and the maximum is $19,297.
• b. To find the average annual cost of repairs over the three years, we sum the total costs and divide by the number of years: ($10,648 + $19,297 + $10,291) / 3 = $40,236 / 3 = $13,412.
• c. If the company wants a one-year balance in the self-insurance account that is 10 percent higher than the highest annual cost of repairs, they should target $(19,297 * 1.10) = $21,226.80 in total. To save this amount in 12 months, they need to save $21,226.80 / 12 = $1,768.90 per month.

This process can help Bowman Co. make an informed decision about whether to self-insure or purchase an insurance policy by comparing the potential savings against the possible risks and costs.