Question

Suppose the probability that a person will die in the next 20 years is 8.2698%. This person has a life insurance policy that will pay out $70,000 to the beneficiaries of the policy if the person dies in the next 20 years. The administrative costs of the policy are $85. What is the premium of the policy?

A) $5788.86
B) $5873.86
C) $70,000
D) $5703.86

Answer 1

The premium of the life insurance policy is calculated by multiplying the probability of death (8.2698%) by the pay-out amount ($70,000) plus administrative costs ($85), resulting in a premium of $5,873.86 which corresponds to option B.

Step-by-step explanation:

The question asks us to calculate the premium of a life insurance policy based on the given probability of an event (death) occurring within a specific time frame (20 years), and a specified pay-out amount ($70,000) with additional administrative costs ($85).

To calculate the premium, we need to consider how insurance companies use probability to determine premium prices. The premium should cover the expected pay-out which is determined by the probability of the event occurring within the policy term, plus administrative costs. The expected pay-out is the product of the pay-out amount and the probability of death.

In this case, the expected pay-out would be 0.082698 (probability of death) multiplied by $70,000 (pay-out amount). This result is then added to the administrative costs to get the total premium:

• Expected pay-out = Probability of death × Pay-out amount.
  Expected pay-out = 0.082698 × $70,000 = $5,788.86
• Total premium = Expected pay-out + Administrative costs
  Total premium = $5,788.86 + $85 = $5,873.86

Therefore, the correct premium for the policy would be $5,873.86, which corresponds to option B.