2005年11月那场精算师北美SOA真题ExamM（第六部分），供大家备战10月份左右的考试专用。
　　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 ? = , 30 x ≥
　　(ii) For smokers, ( ) 0.16, s x ? = 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
　　高顿网校之名人心语：青年人的性格如同一匹不羁的野马，藐视既往，目空一切，好走极端，勇于革新而不去估量实际的条件和可能性，结果常因浮躁而改革不成却招致更大的祸患，老年人则正相反。他们常常满足于困守已成之局，思考多于行动，议论多于果断，为了事后不后悔，宁肯事前不冒险。