An automotive insurance company has 30,000 policyholders, and the accident rate is 0.06. if the company needs to make a profit of $1,740,000 this year and the payout for each claim (after deductibles) is $8,200, the minimum premium it must charge is

Number of accidents = number of policyholders * accident rate = 30,000 * 0.06 = 1,800

Total payout = payout per each claim * number of claims

Number of claims = number of accidents

=> Total payout = $8,200 * 1,800 =   $ 14,760,000

Total minimum premium = total payout + profit = $ 14,760,000 + $ 1,740,000 = $ 16,500,000.

Minimum premum charge = total minimum premum / number of policyholders

Minimum premium charge = $ 16,500,000 / 30,000 =  $550

$ 550