Answer:
The minimum premium charge = $550
The minimum premium increased by $18.4
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 ...