Expected Value: Live Insurance Jim is a 60-year old male in reasonably good heal
ID: 449355 • Letter: E
Question
Expected Value: Live Insurance
Jim is a 60-year old 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 Setion of the Statistical Abustract of the United States (116th Edition).
x = age 60 61 62 63 64
P(death at this age 0.01191 0.01292 0.01396 0.01503 0.01613
Jim is applying to Big Rock Insuarance Company for his term insurance policy.
a) What is the probability that Jim will die in his 60th year? Using this probability and the $50,000 death benefit, 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 year 60 through 64?
c) Interpretation: 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 a charge for the polciy?
d) Interpretation: If Big Rock Insurance Comapny charges $5000 for the policy, how much profit does the company expect to make?
Please solve and show your work, thank you.
Explanation / Answer
a) The probability that Jim will die at the age of 60 is p(60) = 0.01191.
The expected loss of Big Rock insurance is p(60)*50,000 =0.01191*50,000
EV = -$ 595.5
b) Repeat part (a) for years 61, 62, 63, and 64. What would be the total expected cost to big Rock Insurance over the year 60 through 64?
The total expected loss is 3497.5
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 a charge for the polciy?
To make profit of 700 above teh expected total cost paid out Jim's death Big Rock should charge minimum of
3497.5 + 700 = $4197.5
d) If Big Rock Insurance Comapny charges $5000 for the policy, how much profit does the company expect to make?
The company expects to make $5000 - 3497.5 = $1502.5
x=Age p(death at this age) Expected loss =p*50,000 60 0.01191 = 0.01191*50,000= 595.5 61 0.01292 =0.01292*50,000= 646.0 62 0.01396 =0.01396*50,000= 698.0 63 0.01503 =0.01503*50,000= 751.5 64 0.01613 =0.01613*50,000= 806.5 Total 3497.5Related Questions
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