Question

Suppose that a life insurance company insures 5,100 40-year-old people in a given year. Assume the death rate of 4 per 100 people. The cost of the premium is $100 per year, and the death benefit is $45,000. How much can the company expect to gain in a year?

A) $1,890,000
B) $1,764,000
C) $2,160,000
D) $1,980,000

Answer 1

To calculate the expected gain for the insurance company, multiply the number of insured people by the death rate to find expected deaths, then calculate the total death benefits paid and subtract this from the total premiums received. The expected gain is $1,890,000.

Step-by-step explanation:

The student asked how much a life insurance company can expect to gain in a year if it insures 5,100 40-year-old people at a cost of $100 premium per year and a death benefit of $45,000, given a death rate of 4 per 100 people.

To calculate the expected gain, first determine the expected number of deaths by multiplying the total number of people insured by the death rate:
5,100 people * (4/100) = 204 expected deaths.

Next, calculate the total death benefits paid: 204 deaths * $45,000 = $9,180,000. Then, calculate the total premiums received: 5,100 people * $100 = $510,000. Finally, subtract the total death benefits from the total premiums to find the expected gain:

$510,000 - $9,180,000 = $1,890,000 expected gain. Therefore, the answer is Option A: $1,890,000.