Expected Value: Life Insurance Sara is a 60-year-old female in reasonably good health. She wants to take out a $50,000 term (that is, straight death benefi t) life insurance policy until she is 65.

The policy will expire on her 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116th Edition).

x  age 60 61 62 63 64 P(death at this age) 0.00756 0.00825 0.00896 0.00965 0.01035 Sara is applying to Big Rock Insurance Company for her term insurance policy.

(a) What is the probability that Sara will die in her 60th year? Using this probability and the $50,000 death benefi t, what is the expected cost to Big Rock Insurance?

(b) Repeat part

(a) for years 61, 62, 63, and 64.

What would be the total expected cost to Big Rock Insurance over the years 60 through 64?

(c) Interpretation If Big Rock Insurance wants to make a profi t of $700 above the expected total cost paid out for Sara’s death, how much should it charge for the policy?

(d) Interpretation If Big Rock Insurance Company charges $5000 for the policy, how much profi t does the company expect to make?