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UNSW
ACTL1001 Actuarial Studies and Commerce
Solutions 12 and Revision
Exercise 1
Expected salary at age 65 for a 20 year old. Actual salary will
be
45
;
000
e
P
45
i
=1
&
i
where
&
i
&
Normal
(0
:
04
;
0
:
01)
and we use the
&
(
±;²
)
notation. Since each
&
i
is independent we
know that
P
45
i
=1
&
i
&
(45
±
0
:
04
;
p
45
±
0
:
01)
Therefore expected salary is
45
;
000
e
45
&
0
:
04+
1
2
&
45
&
0
:
01
2
= 45
;
000
e
1
:
80225
= 45
;
000
±
6
:
0632745
= 272
;
847
Exercise 2
Expected present value. First determine expected retirement ben
e&t at age 65 in 20 years time (age 45 currently). Expected salary is
55
;
000
e
20
&
0
:
04+
1
2
&
20
&
0
:
01
2
= 55
;
000
e
0
:
801
= 55
;
000
±
2
:
2277676
= 122
;
527
:
22
Service to age 65 will be 40 years so (20 years current service plus 20 years
future service). Expected bene&t at age 65 will be
8
±
40
60
±
122
;
527
:
217 = 653
;
478
:
49
and the present value factor will be
1
(1
:
06)
20
= 0
:
311805
Hence the expected present value of the retirement bene&t is
0
:
75
±
0
:
311805
±
653
;
478
:
49 = 152
;
818
since 0.75 is the probability of payment of the bene&t at retirement.
1
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View Full DocumentExercise 3
An actuarial review of a de&ned bene&t superannuation fund
usually involves determining if the assets that are accumulating in the fund
will be su¢ cient, along with future contributions, to meet the bene&t pay
ments. It also will involve an assessment of the adequacy of the contribution
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