30. For a fully discrete whole life insurance of 1000 on (45), you are given:
t 45 1000tV 45 t q +
22 235 0.015
23 255 0.020
24 272 0.025
Calculate 25 45 1000 V .
(A) 279
(B) 282
(C) 284
(D) 286
(E) 288
Exam M: Fall 2005 -31- GO ON TO NEXT PAGE
31. The graph of a piecewise linear survival function, ( ) s x , consists of 3 line segments with
endpoints (0, 1), (25, 0.50), (75, 0.40), (100, 0).
Calculate 15 20 55
55 35
q
q
.
(A) 0.69
(B) 0.71
(C) 0.73
(D) 0.75
(E) 0.77
Exam M: Fall 2005 -32- GO ON TO NEXT PAGE
32. For a group of lives aged 30, containing an equal number of smokers and non-smokers, you
are given:
(i) For non-smokers, ( ) 0.08 n x µ = , 30 x ≥
(ii) For smokers, ( ) 0.16, s x µ = 30 x ≥
Calculate 80 q for a life randomly selected from those surviving to age 80.
(A) 0.078
(B) 0.086
(C) 0.095
(D) 0.104
(E) 0.112
Exam M: Fall 2005 -33- GO ON TO NEXT PAGE
33. For a 3-year fully discrete term insurance of 1000 on (40), subject to a double decrement
model:
(i)
x ( )
x l τ ( ) 1
x d ( ) 2
x d
40 2000 20 60
41 − 30 50
42 − 40 −
(ii) Decrement 1 is death. Decrement 2 is withdrawal.
(iii) There are no withdrawal benefits.
(iv) 0.05 i =
Calculate the level annual benefit premium for this insurance.
(A) 14.3
(B) 14.7
(C) 15.1
(D) 15.5
(E) 15.7
Exam M: Fall 2005 -34- GO ON TO NEXT PAGE
34. Each life within a group medical expense policy has loss amounts which follow a compound
Poisson process with 0.16 λ= . Given a loss, the probability that it is for Disease 1 is 1
16 .
Loss amount distributions have the following parameters:
Mean per loss
Standard
Deviation per loss
Disease 1 5 50
Other diseases 10 20
Premiums for a group of 100 independent lives are set at a level such that the probability
(using the normal approximation to the distribution for aggregate losses) that aggregate
losses for the group will exceed aggregate premiums for the group is 0.24.
A vaccine which will eliminate Disease 1 and costs 0.15 per person has been discovered.
Define:
A = the aggregate premium assuming that no one obtains the vaccine, and
B = the aggregate premium assuming that everyone obtains the vaccine and the cost of the
vaccine is a covered loss.
Calculate A/B.
(A) 0.94
(B) 0.97
(C) 1.00
(D) 1.03
(E) 1.06
Exam M: Fall 2005 -35- GO ON TO NEXT PAGE
35. An actuary for a medical device manufacturer initially models the failure time for a particular
device with an exponential distribution with mean 4 years.
This distribution is replaced with a spliced model whose density function:
(i) is uniform over [0, 3]
(ii) is proportional to the initial modeled density function after 3 years
(iii) is continuous
Calculate the probability of failure in the first 3 years under the revised distribution.
(A) 0.43
(B) 0.45
(C) 0.47
(D) 0.49
(E) 0.51
Exam M: Fall 2005 -36- GO ON TO NEXT PAGE
36. For a fully continuous whole life insurance of 1 on (30), you are given:
(i) The force of mortality is 0.05 in the first 10 years and 0.08 thereafter.
(ii) 0.08 δ=
Calculate the benefit reserve at time 10 for this insurance.
(A) 0.144
(B) 0.155
(C) 0.166
(D) 0.177
(E) 0.188
Exam M: Fall 2005 -37- GO ON TO NEXT PAGE
37. For a 10-payment, 20-year term insurance of 100,000 on Pat:
(i) Death benefits are payable at the moment of death.
(ii) Contract premiums of 1600 are payable annually at the beginning of each year for 10
years.
(iii) i = 0.05
(iv) L is the loss random variable at the time of issue.
Calculate the minimum value of L as a function of the time of death of Pat.
(A) − 21,000
(B) − 17,000
(C) − 13,000
(D) − 12,400
(E) − 12,000
Exam M: Fall 2005 -38- GO ON TO NEXT PAGE

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