Final answer:
To reach an expected profit of $100 per policy, the insurance company should charge each driver a premium of $1,960 after calculating for both the costs of accidents and the desired profit.
Step-by-step explanation:
To calculate the premium that the company should charge to have an expected value of $100 per policy, you need to consider the total costs of the accidents and the expected profit. The company wants to cover $186,000 in accidents costs with 100 drivers, and also make $100 in profit per driver. To find the required premium, calculate the total amount of money needed by the company by adding the accident costs to the total expected profit ($186,000 + $100 × 100 drivers).
Total needed = $186,000 + ($100 × 100) = $186,000 + $10,000 = $196,000
Now, divide the total amount by the number of drivers to find the premium per driver.
Premium per driver = Total needed / Number of drivers = $196,000 / 100 = $1,960
Therefore, the company should charge each driver a premium of $1,960 to reach their expected value of profit.