Faculty of Actuaries Institute of Actuaries
EXAMINATIONS
April 1999
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 14 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—A99 ã Institute of Actuaries
A2(A)—2
PART ONE
For questions 1–7 indicate in your answer booklet which one of the answers A, B, C or D
is correct.
1 Using A1967–70 mortality, which of the following gives the value of 3 2 45 1 q + ?
A 0.008927
B 0.008943
C 0.012683
D 0.012705 [2]
2 Which of the following is the value of A60 5 : using a(55) males mortality and
interest at 4% per annum?
A 0.82110
B 0.82715
C 0.83357
D 0.83663 [3]
3 Which of the following is the present value of an endowment assurance policy
issued to a life aged x with term n years, where Tx is the future lifetime of (x)?
A
v T n
v T n
T
x
n
x
x <
³
RST
B
v T n
v T n
n
x
T
x
x
<
³
RST
C
0 T n
v T n
x
n
x
<
³
RST
D
v T n
T n
T
x
x
x <
³
RST
0
[2]
A2(A)—3 PLEASE TURN OVER
4 Which of the following formulae are correct?
I (IA)x:n
1 =
S
k
n
x k x n
x
M n M
D
=
-
+ + -
0
1
.
II (IA)x:n
1 =
S
k
n
x k
x
k C
D
=
-
+ +
0
1
( 1) .
III (IA)x:n
1 = (IA)x -
D
D x
n
x
+ . (IA)x+n
A I and II only.
B II and III only.
C I only.
D III only. [2]
5 A life aged 50 effects a with profit whole life assurance with sum assured of
£1,000 plus attaching bonuses, payable immediately on death. Assuming
allowance for compound bonuses of 1.9231% per annum, vesting at the start of
each policy year, which of the following gives the closest approximation to the
single premium payable?
Basis: Mortality A1967–70 (ultimate)
Interest 6% per annum
Expenses none
A £384.50
B £388.40
C £392.11
D £395.87 [3]
6 Which of the following is equal to the expression:
s x x s x s
w
x
w
p ds ds - + - FHIK
z m exp z m where x > 0 and w > x
A sqx
B spx
C 1
D 2 [2]
A2(A)—4
7 A one year term assurance is issued to a life aged 60 for a sum assured of
£50,000 payable at the end of the policy year of death. Which of the following
gives the standard deviation of the present value of the term assurance, using
A1967–70 (select) mortality and 8% per annum interest?
A 3,403
B 3,777
C 4,235
D 5,522 [3]
PART TWO
8 Let W be the random variable representing the present value of an annuity of
£100 per annum paid continuously to a life now aged exactly x until death.
Find an expression for Var(W) in terms of whole of life assurance functions. [4]
9 (i) Show that (tVx + Px) (1 + i) = (px+t) (t+[1] [2] [3] 下一页 |
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