Question

Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (i.e., straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided. x = age 60 61 62 63 64 P(death at this age) 0.01078 0.01441 0.016510.02065 0.02236 Jim is applying to Big Rock Insurance Company for his term insurance policy. (a) What is the probability that Jim will die in his 60th year? (Enter a number. Enter your answer to five decimal places.) Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance in dollars)? (Enter a number. Round your answer to two decimal places.) (b) What is the expected cost to Big Rock Insurance for years 61, 62, 63, and 64 (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.) year 61 $ year 62 $ year 63 $ year 64 $ What would be the total expected cost to Big Rock Insurance over the years 60 through 64 (in dollars)? (Enter a number. Round your answer to two decimal places.) (c) If Big Rock Insurance wants to make a profit of $700 above the expected total cast paid out for Jim's death, how much should it charge for the policy (in dollars)? (Enter a number. Round your answer to two decimal places.) (d) If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make (in dollars)? (Enter a number. Round your answer to two decimal places.)

Answer 1

a). Probability that Jim will die in his 60th year = 0.01078 (reading from the given table)

b Cost to the insurance company if Jim dies in the 60th year = probabaility of death*death benefit

= 0.01078*50,000 = 539.00

c). Expected cost for years 61, 62, 63 and 64 are, as given in the table below:

Formula x = age 69 DB Prob(death at age x) Death benefit 0.01078 50000 0.01441) 0.01651 50000 0.02065 50000 0.02236 50000 EC =P*DB Expected cost 539.00 720.50 825.50 1032.50 1118.00 3696.50 62 64 Total cost

Total expected cost = 3,696.50

d). For a profit of $700, Big Rock should charge 3,696.50 + 700 = 4,396.50

e). Profit = 5,000 - 3,696.50 = 1,303.50