Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out

Question

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).

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.)
$  

(b) Repeat part (a) for years 61, 62, 63, and 64. (Round your answers to two decimal places.)

What would be the total expected cost to Big Rock Insurance over the years 60 through 64? (Round your answer to two decimal places.)
$  

(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.)
$  

(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.)
$

Explanation / Answer

1(a) The probability that Jim will die in his 60th year = Pr ( death at 60 age) = 0.01123.

       and Using this probability and the $50,000 death benefit,

       the expected cost to Big Rock Insurance = $50000 * 0.01123 = $561.50

1(b)

P(death in year 61) = 0.01357             Expected cost = $678.50

P(death in year 62) = 0.01744               Expected cost = $872.00

P(death in year 63) = 0.01915               Expected cost = $957.50

                   P(death in year 64) = 0.02368               Expected cost = $1184.00

the total expected cost to Big Rock Insurance over the years 60 through 64

Total expected cost = $561.5 + $678.5 + $872 + $957.5 + $1184 = $ 4253.5.

1(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?

$ 4253.5 + $ 700 = $ 4953.5 or $ 82.56 per month.

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

$ 5000 - total expected cost = $746.5 per policy

Thank you...

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