Faculty of Actuaries Institute of Actuaries
EXAMINATIONS
April 1998
Subject A — Fundamentals of Actuarial Mathematics
Paper Two
Time allowed: Three hours
INSTRUCTIONS TO THE CANDIDATE
1. Write your surname in full, the initials of your other names and your
Candidate’s Number on the front of the answer booklet.
2. Begin your answers to Parts One, Two and Three on a separate sheet.
3. Mark allocations are shown in brackets.
4. Attempt all 16 questions.
Graph paper is not required for this paper.
AT THE END OF THE EXAMINATION
Hand in BOTH your answer booklet and this question paper.
In addition to this paper you should have available
Actuarial Tables and an electronic calculator.
ã Faculty of Actuaries
A2—A98 ã Institute of Actuaries
A2(A)—2
PART ONE
For questions 1–8 indicate in your answer booklet which one of the answers A, B, C or D
is correct.
1 Which of the following is equal to the function k½Ax:n
1 ?
I D
D
x k A A
x
x k x k n
+
+ + + ( - )
II D
D
x k v q
x h
n
h
h x k
+
=
-
+
+ S ½
0
1
1 .
III S
h k
n
h
h x x h v p q
= +1 -1 + -1 . .
A I and II are correct
B II and III are correct
C I only is correct
D III only is correct [3]
2 Which of the following is the value of A[35]:10
1 , using A1967–70 mortality, with
interest at 6% p.a.?
A 0.00974
B 0.00995
C 0.01010
D 0.01053 [3]
3 Which of the following is the probability that a female aged exactly 62 will live
to age 67 but die before reaching age 70, assuming a(55) select mortality?
A 0.05204
B 0.05225
C 0.08123
D 0.08180 [2]
A2(A)—3 PLEASE TURN OVER
4 Which of the following is ¶
¶x
p t x ?
A t px . (mx - mx t ) +
B t x x t x p . (m m ) + -
C t x x t p . m +
D - t x x +t p . m [2]
5 Which of the following is equal to 10V45:25 ?
A
1
55
55 70 70
45 70 70 55 70
45 70 D
M M D
M M D N N
N N
- + -
- + -
-
FHG
IKJ
( )( )
( )
B
1
55
55 70
55 70 55 70
45 70 D
M M
M M N N
N N
- -
- -
-
FHG
IKJ
( )( )
( )
C
1
45
45 70 70
45 70 70 45 55
45 70 D
M M D
M M D N N
N N
- + -
- + -
-
FHG
IKJ
( )( )
( )
D
1
45
45 70
45 70 45 55
45 70 D
M M
M M N N
N N
- -
- -
-
FHG
IKJ
(

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