A 60-year-old buys a 1-year term life insurance policy worth $1000 and it costs him $60. If his likelihood of living to age 61 is 0.972, what is the expected value of the policy?
The expected value of the policy is the sum of the products of the possible outcomes and their probabilities. In this case, there are two possible outcomes: the insured lives to age 61 and the insured dies before age 61.
The probability of the insured living to age 61 is 0.972, so the probability of the insured dying before age 61 is 1 - 0.972 = 0.028.
If the insured lives to age 61, he will not receive any payout from the policy, so the value of this outcome is 0.
If the insured dies before age 61, he will receive a payout of $1000, but he will have paid $60 in premiums. Therefore, the value of this outcome is $1000 - $60 = $940.
The expected value of the policy is:
(0.972 x 0) + (0.028 x $940) = $26.32
Therefore, the expected value of the policy is $26.32.
To calculate the expected value of the policy, we need to multiply the potential outcomes by their probabilities and then sum them up.
In this case, there are two potential outcomes:
1. The policyholder dies before reaching age 61, resulting in a payout of $1000.
2. The policyholder lives to age 61, resulting in no payout.
Let's calculate the expected value step by step:
1. Calculate the probability of the policyholder dying before reaching age 61:
Probability of dying = 1 - Probability of living = 1 - 0.972 = 0.028
2. Calculate the expected payout for the first outcome:
Payout if policyholder dies = $1000
Expected payout = Probability of dying * Payout if policyholder dies = 0.028 * $1000 = $28
3. Calculate the payout for the second outcome:
Payout if policyholder lives = $0
4. Calculate the expected value of the policy:
Expected value = Expected payout for the first outcome + Payout for the second outcome = $28 + $0 = $28
Therefore, the expected value of the policy is $28.
To calculate the expected value of the policy, we need to multiply the payout amount by the probability of receiving that payout. Here's how you can calculate it step-by-step:
Step 1: Calculate the expected payout if the insured individual dies before reaching age 61.
The payout in this case is $1000. Since the probability of living to age 61 is 0.972, the probability of dying before age 61 is 1 - 0.972 = 0.028.
Expected payout if the insured individual dies before reaching age 61 = $1000 * (0.028) = $28
Step 2: Calculate the expected payout if the insured individual lives to age 61.
In this case, there is no payout because the policy is a 1-year term policy, and the insured individual is alive at the end of the policy term.
Expected payout if the insured individual lives to age 61 = $0
Step 3: Calculate the expected value of the policy.
The expected value is calculated by adding up the expected payouts in both cases.
Expected value of the policy = Expected payout if the insured individual dies before reaching age 61 + Expected payout if the insured individual lives to age 61
= $28 + $0
= $28
Therefore, the expected value of the policy is $28.