Expected profit, expected loss and required probability.
Sara is a 60 year old Anglo female in reasonably good health. She wants to take out a $50,000 term (that is, straight death benefits) life insurance policy until she is 65. The policy will expire on her 65^{th} birthday. The probability of death in a given year is provided by the Vital Statistics section of the Statistical Abstract of the United States.
X = Age (years)

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 likelihood that Sara will die in her 60^{th} year? Using this probability and the $50,000 death benefit, what is the expected loss to Big Rock Insurance?
b. Repeat part (a) for years 61, 62, 63 and 64. What would be the total expected loss to Big Rock Insurance over the year 60 during 64?
c. If Big Rock Insurance wants to make a profit of 5700 above the expected total loss paid out for Sara's death, how much should it charge for the policy?
d. If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make?