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)	0.01084	0.01345	0.01657	0.02071	0.02314

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

SOLUTION:

From given data,

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.

(a) (i) What is the probability that Jim will die in his 60th year?

Let X is a random variable defined as the age of death.

From the given information ,the probability that jim will die in the 60th year is given as,

P(X = 60) = 0.01084 (from given table)

therefore , The probability that jim will die in the 60 th year is 0.01084 .

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

From the given information ,Cost = $50,000 and the probability of 60th year is 0.01084

The expected cost to Big Rock insurance is obtained as given below :

Expected cost = Cost * Probability

=$ 50000 *0.01084

Expected cost  = $ 542

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

(b) Repeat part (a) for years 61:

From the given information ,Cost = $50,000 and the probability of 61st year is 0.0134

The expected cost to Big Rock insurance is obtained as given below :

Expected cost = Cost * Probability

=$ 50000*0.0134

Expected cost  = $ 670

(b) Repeat part (a) for years 62:

From the given information ,Cost = $50,000 and the probability of 62nd year is 0.01657

The expected cost to Big Rock insurance is obtained as given below :

Expected cost = Cost * Probability

=$ 50000*0.01657

Expected cost  = $ 828.5

(b) Repeat part (a) for years 63:

From the given information ,Cost = $50,000 and the probability of 63rd year is 0.02071

The expected cost to Big Rock insurance is obtained as given below :

Expected cost = Cost * Probability

=$ 50000*0.02071

Expected cost  = $ 1035.5

(b) Repeat part (a) for years 64:

From the given information ,Cost = $50,000 and the probability of 64 th year is 0.02314

The expected cost to Big Rock insurance is obtained as given below :

Expected cost = Cost * Probability

=$ 50000*0.02314

Expected cost  = $ 1157

(b)(ii)What would be the total expected cost to Big Rock Insurance over the years 60 through 64?

E(Total cost) = [ E(X=60) + E(X=61) + E(X=62) + E(X=63) + E(X=64) ]

= [ 542 + 670 + 828.5 + 1035.5 + 1157 ]

E(Total cost) = $ 4233

(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?

From the given information , the total profit is $700

The total expected cost is $ 4233

The charge for the policy is obtained as given below

Profit = Charges - Total expected cost

$700 = Charges - $ 4233

Charge = $(700 + 4233)

Charge  =$4933

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

From the given information , the total charge is $5000

The total expected cost is $ 4233

The charge for the policy is obtained as given below

Profit = Charges - Total expected cost

= Charges - $ 4233

= 5000 - 4233

Profit  =$767