Final answer:
The expected value of the $200,000 1-year term life insurance policy sold to a 42-year-old male for $670, with a survival probability of 0.99748, is $166.38. This figure represents the average profit the insurance company expects to make per policy, given the probability of the insured individual's death.
Step-by-step explanation:
To compute the expected value of a $200,000 1-year term life insurance policy sold to a 42-year-old male for $670 with a survival probability of 0.99748, we need to consider two outcomes: the man survives, or the man dies within the year.
If the man survives, which has a probability of 0.99748, the insurance company will make $670, because they do not need to pay out the death benefit. On the other hand, if the man dies, which has a probability of 1 - 0.99748 = 0.00252, the company loses $200,000 but keeps the premium, totaling a loss of $199,330.
The expected value (EV) can be calculated as follows:
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- EV = (Probability of Survival x Profit if Survives) + (Probability of Death x Loss if Dies)
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- EV = (0.99748 x $670) + (0.00252 x -$199,330)
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- EV = $668.71 - $502.33
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- EV = $166.38
The expected value to the insurance company for this policy is $166.38. This means that, on average, the insurance company expects to earn $166.38 on policies of this type after accounting for the probability of paying out death benefits.