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 $.
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The minimum premium charge = $550

The minimum premium increased by $18.4

Step-by-step explanation:

Policyholders = 30,000

Accident rate = 0.06

Number of accidents = 30,000*0.06 = 1800

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

Total payout = pay out per each claim * number of claims

Total payout = 8200 * 1800 = $ 14,760,000

Now total minimum premium = total payout + profit

= $ 14,760,000+ $1,740,000

= $ 16,500,000.

Minimum premium charge = total minimum premium / number of policyholders

= $ 16,500,000/30,000

= $550

Thus the minimum premium charge = $550

B) The accident rate will increase by 5% = 1.05

multiply the previous accident rate with this rate

0.06*1.05 = 0.063

Accident rate = 0.063

Number of policy holders will increase 12% = 1.12

30,000*1.12 = 33600

Number of accidents = 33600*0.063 = 2116.8

Total payout = payout per each claim * number of claims

8200 *2116.8 = $ 17357760

Total minimum premium = total payout + profit

= $ 17357760 + $ 1,740,000 = $19,097,760

Minimum premium charge = total minimum premium / number of policyholders

Minimum premium charge = $ 19,097,760 / 33600=  

568.4 - 550

= 18.4

The minimum premium increased by $18.4 ...

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step-by-step explanation: