Examples
Doug is 18 years old and buys an insurance policy that
pays $100 if he dies in the first year, $200 if he dies in the
second year, $150 if he dies in the third year, and $200 if
he survives to the end of the three years. Payments are
made at the end of the year of death/survival. Premiums
are paid annual in advance. The insurer pays initial
expenses of $10, as well as premium expenses of $5 + 2%
of each premium received. The interest rate is 6% p.a.
and
p
18
= 0
.
7
,
p
19
= 0
.
6
,
p
20
= 0
.
5
,
p
21
= 0
.
4
1.
Explain why Doug’s benefits can be expressed as
50
A
18
:
1
3

{z
}
8
.
8160
+ 150
A
18
:
3

{z
}
132
.
7287
+ 50
A
1
18
:
2

{z
}
26
.
6109

100
A
1
18
:
1

{z
}
28
.
3019
= 139
.
8537
2.
Show that the fair premium is
P
= 80
.
2735
.
3.
Show that the reserves for this policy are
1
V
= 53
.
5544
,
2
V
= 91
.
4263
,
3
V
= 200. Hint:
(
t
V
+
P

Exp
t
)(1+
i
) = (
q
x
+
t
)Ben
t
+1
+(
p
x
+
t
)
t
+1
V
UNSW Week 10 ACTL1001 Tutorial
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Examples
Benefits
Draw a diagram! 150
A
18
:
3
represents receiving $150 at the end of
the year of death for the next 3 years, or survival for the next 3
years. Since Doug should receive $200 in total on survival, we need
to add 50
A
18
:
1
3
. Similarly, since he receives $200 if he dies during
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 One '09
 Nicole
 Actuarial Science, Education in Scotland, Doug, ACTL1001 Tutorial

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