Final answer:
Charging an actuarially fair premium per risk group allows an insurance company to break even by aligning premiums to the risk level of each group. Charging a one-size-fits-all premium can result in financial losses as low-risk drivers may leave and high-risk drivers dominate the pool. Correct classification and premium assignment are essential for the company's financial stability.
Step-by-step explanation:
An insurance company must carefully calculate premiums to cover the expected collision payment costs while allowing the company to operate without a loss. If the company charges the actuarially fair premium to the entire group rather than to each risk group separately, it risks charging low-risk drivers too much and high-risk drivers too little. This mismatch may result in the departure of low-risk drivers (who may find cheaper insurance elsewhere), leaving the company with a pool of high-risk drivers. Consequently, the insurance company's costs may exceed its premiums, leading to financial losses.
If the insurance company correctly classifies drivers according to risk group and assigns premiums based on expected losses, the premium will more accurately reflect the true cost of insuring each driver. For instance, if the company charges safer drivers less and riskier drivers more, it aligns the premiums with the actual risk, creating an actuarially fair system. Therefore, to break even, a company needs to collect a total amount in premiums that equals the expected payout for claims, which would be $186,000 in the example provided. Charging each of the 100 drivers a $1,860 premium yearly achieves this break-even point.