Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (that is, 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 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) 0.01036 0.01480 0.01600 0.02032 0.02230 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 your answer to five decimal places.) Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance? (Round your answer to two decimal places.) FIND: $
(b) Repeat part (a) for years 61, 62, 63, and 64. (Round your answers to two decimal places.) Year Expected Cost 61 $ 62 $ 63 $ 64 $ What would be the total expected cost to Big Rock Insurance over the years 60 through 64? (Round your answer to two decimal places.) FIND: $
(c) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Jim's death, how much should it charge for the policy? (Round your answer to two decimal places.) FIND: $
(d) If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make? (Round your answer to two decimal places.) FIND: $
The data set provided in the above question is as follows:
| Age (x) | Probability p(x) |
| 60 | 0.01036 |
| 61 | 0.0148 |
| 62 | 0.016 |
| 63 | 0.02032 |
| 64 | 0.0223 |
a) The probability that Jim will die in his 60th year is 0.01036.
Using the probability = 0.01036 and the death benefit = $ 50000.
The expected cost = 0.01036 X $ 50000 = $ 518.00
b) The probailities that jim will die in his 61st year is 0.01480.
The expected cost = 0.01480 X $ 50000 = $ 740.00
The probailities that jim will die in his 62st year is 0.01600.
The expected cost = 0.01600 X $ 50000 = $ 800.00
The probailities that jim will die in his 63rd year is 0.02032.
The expected cost = 0.02032 X $ 50000 = $ 1016.00
The probailities that jim will die in his 64th year is 0.02230.
The expected cost = 0.02230 X $ 50000 = $ 1115.00
Total expected cost from 60 to 64 year = $ 518.00 + $ 740.00 + $ 800.00 + $ 1016.00 + $ 1115.00 = $ 4189.00.
c) The value of profit is calculated as:
Revenue - Cost = Profit
Let, x = Revenue = Amount to be charged for the policy
x - $ 4189.00 = $ 700.00
x = $ 4889.00
d) Given, Revenue = $ 5000.00 = Amount charged for the policy.
Revenue - Cost = Profit
$ 5000.00 - $ 4189.00 = $ 811.00
Hence, the required solutions are given above.
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