Sara is a 60yearold Anglo female in reasonably good health S

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).

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.

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?
$

Solution

a) the probability that sara will die in her 60th year is as given in the table=0.00574

the expected cost to Big rock insurance policy is=probability*amount= 0.00574*50000=$287

b) the probability that sara will die in her 61th year is as given in the table=0.00839

the expected cost to Big rock insurance policy is=probability*amount= 0.00839*50000=$419.5

the probability that sara will die in her 62th year is as given in the table=0.00809

the expected cost to Big rock insurance policy is=probability*amount= 0.00809*50000=$404.5

the probability that sara will die in her 63th year is as given in the table=0.01056

the expected cost to Big rock insurance policy is=probability*amount= 0.01056*50000=$528

the probability that sara will die in her 64th year is as given in the table=0.01063

the expected cost to Big rock insurance policy is=probability*amount= 0.01063*50000=$531.5

hence the table is

the total expected cost from year 60 to 64 is $287+$419.5+$404.5+$528+$531.5=$2170.5   [answer]

c) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Sara\'s death

then total amount is $2170.5+$700=$2870.5

hence it should charge for the policy $2870.5 [answer]

d) If Big Rock Insurance Company charges $5000 for the policy, then expected profit=$5000-expected cost=$5000-$2870.5=$2129.5   [answer]