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.
o;u
To find the number of accidents the company will have to pay out for, you can multiply the number of policyholders by the accident rate:
Number of accidents = Number of policyholders * Accident rate
= 25,000 * 0.07
= 1,750 accidents
To calculate the company's total payouts, you can multiply the number of accidents by the payout for each claim:
Total payouts = Number of accidents * Payout per claim
= 1,750 * $8,000
= $14,000,000
To account for the 8% profit margin, you can multiply the total payouts by the profit margin percentage and add it to the total payouts:
Total premium = Total payouts + (Total payouts * Profit margin)
= $14,000,000 + ($14,000,000 * 0.08)
= $14,000,000 + $1,120,000
= $15,120,000
Finally, to find the maximum amount the company can set aside for this year's investments, you can subtract the total premium from the total payouts:
Maximum investment amount = Total payouts - Total premium
= $14,000,000 - $15,120,000
= -$1,120,000
Since the result is negative, it means that the company does not have enough funds to set aside for investments. They would need additional funds to cover their expenses and maintain the profit margin.
To calculate the number of accidents the company will have to pay out for, you can multiply the total number of policyholders by the accident rate:
Number of accidents = 25,000 * 0.07 = 1,750 accidents
To calculate the total payouts, you can multiply the number of accidents by the payout for each claim:
Total payouts = Number of accidents * Payout per claim = 1,750 * $8,000 = $14,000,000
To determine the premium the company must charge to maintain an 8% profit margin, you need to calculate the profit margin as a percentage of the total payouts:
Profit margin = 8% = 0.08
Profit = Profit margin * Total payouts
Profit = 0.08 * $14,000,000 = $1,120,000
The premium the company must charge is the total payouts plus the profit:
Premium = Total payouts + Profit = $14,000,000 + $1,120,000 = $15,120,000
Lastly, to determine the maximum amount the company can set aside for this year's investments, you need to subtract the total payouts from the premium:
Maximum amount for investments = Premium - Total payouts = $15,120,000 - $14,000,000 = $1,120,000