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).

x = age	60	61	62	63	64
P(death at this age)	0.01105	0.01378	0.01747	0.01915	0.02269

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.)

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.)
$

(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.)
$

Answer 1

a) probability that dies in 60 th year=				0.01105
expected cost = 50000*0.01105=				552.5

b)

probability		expected cost
P(61)=0.01378		50000*0.01378=689
P(62)=0.01747		50000*0.01747=873.5
P(63)=0.01915		50000*0.01915=957.5
P(64)=0.02269		50000*0.02269=1134.5
total expected cost =			4207

c)

total premium charged=proft+expected cost =

4907

d)

Profit =premium charged-expected cost=

793