Question

question 6
4 pts
a 36 year old man in the united states has a 0.236% risk of dying during the next year. an insurance company charges a premium of $389 for a life insurance policy that pays a $188,859 death benefit. what is the expected gain or loss to the man when purchasing the insurance policy?
hint: calculate the expected loss of the premium if the man survives (always a negative value), then subtract the premium from the death benefit and calculate the expected gain to the beneficiaries if the man dies (always a positive value), and then add these two numbers to find the net result. a negative net result should be entered as a negative value in the box below.
note: please avoid rounding numbers in the middle of your calculations. however, round your final answer to two decimal places, before entering it in the box below. a negative final answer indicates an expected loss for purchasing the policy.

Explanation:

Step1: Calculate the probability of survival

The probability of dying \( p = 0.00236\). So the probability of survival \( q=1 - p=1 - 0.00236 = 0.99764\)

Step2: Calculate the expected value for survival

If the man survives, his gain \( X_1=- 389\) (a loss of the premium). The contribution to the expected value from survival is \(X_1\times q=-389\times0.99764\)

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Step3: Calculate the expected value for death

If the man dies, his gain (or his beneficiary's gain) \(X_2=(188859 - 389)=188470\). The contribution to the expected value from death is \(X_2\times p = 188470\times0.00236\)

$$ 188470\times0.00236=444.8892 $$

Step4: Calculate the expected value \(E(X)\)

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Answer:

\(56.81\)