Question

An automotive insurance company has 25,000 policyholders. The accident rate is 0.07.

The number of accidents the company will have to pay out for is _____ . If the payout for each claim (after deductibles) is $8,000, the company’s total payouts will amount to $______. If the company wants to keep a profit margin of 8%, the premium it must charge is $______. The company can set aside a maximum amount of $_______for this year’s investments.

Answer 1

The number of accidents the company will have to pay out for is 1,750. The company’s total payouts will amount to $14,000,000. The premium the company must charge is $14,583,333.33 and the maximum amount the company can set aside for investments is $583,333.33.

Step-by-step explanation:

To determine the number of accidents the company will have to pay out for, we multiply the number of policyholders by the accident rate. Therefore, 25,000 policyholders multiplied by 0.07 equals 1,750 accidents the company will have to pay out for.

To find the company's total payouts, we multiply the number of accidents by the payout amount per claim. So, 1,750 accidents multiplied by $8,000 equals $14,000,000 in total payouts.

To calculate the premium the company must charge to keep a profit margin of 8%, we divide the total payouts by 96% (100% - 8%). So, $14,000,000 divided by 0.96 equals $14,583,333.33, which is the premium the company must charge.

Lastly, to determine the maximum amount the company can set aside for investments, we subtract the total payouts from the premium collected. So, $14,583,333.33 minus $14,000,000 equals $583,333.33, which is the maximum amount the company can set aside for investments.