Question

Sara is a 60-year-old Anglo female in reasonably good health. She wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until she is 65. The policy will expire on her 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)	0.00559	0.00977	0.00839	0.01086	0.01129

Sara is applying to Big Rock Insurance Company for her term insurance policy.

(a) What is the probability that Sara will die in her 60th year? (Use 5 decimal places.)


Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance?
$

(b) Repeat part (a) for ages 61, 62, 63, and 64.

Age	Expected Cost
61	$
62	$
63	$
64	$

What would be the total expected cost to Big Rock Insurance over the years 60 through 64?
$

(c) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Sara's death, how much should it charge for the policy?
$

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

Answer 1

a) probability that dies in 60 th year=		0.00559
expected cost = 50000*0.00559=		279.5

b)

probability		expected cost
P(61)=0.00977		50000*0.00977=488.5
P(62)=0.00839		50000*0.00839=419.5
P(63)=0.01086		50000*0.01086=543
P(64)=0.01129		50000*0.01129=564.5

total expected cost =488.5+419.5+543+564.5=

2295

c)

total premium charged=proft+expected cost =

2995

d)

Profit =premium charged-expected cost=

2705