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)	0.01138	0.01309	0.01645	0.01942	0.02287

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) using the given probability distribution table, the probability that Jim will die in his 60th year is 0.01138

Expected value = x*P(x)

where x = $50,000 and P(x)= 0.01138

this implies

E[x] = $50,000*0.01138 = $569.00

(B)

Expected value for 61st year = x*P(x)

where x = $50,000 and P(x)= 0.01309

this implies

E[61] = $50,000*0.01309 = $654.5

Expected value for 62nd year = x*P(x)

where x = $50,000 and P(x)= 0.01645

this implies

E[62] = $50,000*0.01645 = $822.5

Expected value for 63rd year = x*P(x)

where x = $50,000 and P(x)= 0.01942

this implies

E[63] = $50,000*0.01942 = $971

Expected value for 64th year = x*P(x)

where x = $50,000 and P(x)= 0.02287

this implies

E[64] = $50,000*0.02287 = $1143.5

Total expected cost = E[60] +E[61] + E[62] + E[63] + E[64]

= $569 + $654.5+$822.5 + $971+$1143.5

=   $4160.50

(C) If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Jim's death, then they must charge total expected cost plus $700

this implies

= $4160.5 + $700

= $4860.50

(D) total charge per policy = $5000

Total expected cost = $4160.50

Net profit = total charge - expected cost

= $5000 - $4160.5

= $839.50