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FIN 3220A Actuarial Models I
First Term 20052006
Assignment 3
Hand in the solutions on or before 16 November 2005.
1.
A 3year life annuitydue to (
x
) is defined by the following table:
Year
t
Amount of Payment
p
x
+
t
0
1
0.80
1
2
0.75
2
3
0.50
You are given that
v
= 0.9 and that the expected present value of the payments is
K
. Calculate
the probability that the present value of the payments actually made will exceed
K
.
2.
For a 3year temporary life annuitydue on (30), you are given:
•
()
1
,
0
80.
80
x
sx
x
=−
≤ ≤
•
i
= 0.05.
•
1
3
0,1,2,
3, 4,5,
K
aK
Y
+
=
⎧
=
⎨
=
⎩
±±
…
.
Calculate Var(
Y
).
3.
You are given:
•
( )
4
17.287.
a
∞
=
•
0.1025.
x
A
=
•
Deaths are uniformly distributed over each year of age.
Calculate
( )
4
x
a
.
4.
Denote
Z
as the present value random variable for a special benefit on (30). This benefit
provides the following:
•
A life income of 1,000 per year payable continuously while (30) survives.
•
An insurance of 5,000 payable at the moment of death of (30).
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 Spring '05
 CSWong
 Annuity

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