1
FIN 3220A Actuarial Models I
First Term 20052006
Assignment 4
Hand in the solutions on or before 5 December 2005.
1.
You are given the following information:
•
0.19
x
A
=
.
•
2
0.064
x
A
=
.
•
d
= 0.057.
•
0.019
x
π =
.
Here,
π
x
is the gross annual premium the insurer charges per $1 of whole life coverage. What
is the minimum number of policies the insurer must issue to people aged
x
so that the
probability of a positive total loss on the policies issued is less than or equal to 0.05?
2.
A deferred annuity is issued to (55) for an annual income of 10,000 commencing at age 65.
Net annual premiums are to be paid during the deferred period. The death benefit during the
premium paying period is the return of the net annual premiums without interest. You are
given:
•
55:10
8
a
=
±±
.
•
55
12
a
=
±±
.
•
(
)
1
55:10
2.5
IA
=
.
The death benefit is payable at the end of the year of death. Calculate the net annual premium.
3.
You are given:
•
Deaths are uniformly distributed over each year of age.
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 Spring '05
 CSWong
 Actuarial Science, Endowment policy, annual premium, level annual premium

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