1.
A new participant in a pension plan, age 45, has a choice of two benefit
options:
(a)
A defined contribution plan with contributions of 20% of salary each year.
Contributions are made at the beginning of each year and earn 5% per year.
Accumulated cont

1.
A pension plan has one participant currently age 30. You are given:
(a)
Contributions are equal to 2% of salary
(b)
The salary scale Sy is constant within any year of age and Sy=(1.1)y
(c)
The participant's current salary is $40,000
(d)
All contributio

ACMA 425: Practice Final
1.
Determine the actuarial present value of a continuous life annuity to (xy) which
pays $1 per annum while both lives survive, reducing to 1/2 on the death of (y)
and to 1/3 on the death of (x), given:
2.
The retirement income be

Insurance Benefits
:
Axy =
=
=
=
= Ax + Ay - Axy
Annuity Benefits
:
=
=
=
=
=
Formulas connecting insurances and annuitys also apply here.
Variance formulas can also be obtained.
Where 2Axy = Axy determined with replaced by
(ie. vt replaced by v2t)
Contin

ACMA 425: Lecture 3
Joint Life Functions Under Uniform Distribution of Deaths (UDD)
Under UDD for T(x) and T(y)
:
Then,
=
= tpy qx + tpx qy
= (1 - t qy)qx + (1 - t qx)qy
= qx + qy - qx qy + (1-2t)qx qy
=
One can show that
can be approximated by
If we assu

Central Rates of Multiple Decrement
:
Recall for a single decrement,
mx =
=
For multiple decrements,
=
=
mx(j) =
=
Example 2 For a multiple decrement table, you are given:
1.
2.
Calculate mx(1)
Answer:
Associated Single Decrement Tables
:
Definition:
and

ACMA 425: Lecture 1
Multiple Life Functions
General notation
:
u =
q =
t u
q =
t| u
Definition of Failure of a status is necessary in order to compute probability
functions. For example:
(xy) =
=
Joint Life Status
:
T(xy) =
FT(t) =
=
= 1-P[T(xy) >t]
=
=
=

ACMA 425: Lecture 4
Multiple Decrement Models
Multiple Decrements
:
Individual (x) is subject to several causes of decrement which are independent.
Eg. Failure due to death, disability or laps, analysis of mortality by cause of
death, etc.
Model
T(x)
=
T(

1.
(DO NOT HAND IN: Text: 10.11, 10.13, 10.14, 10.15, 10.26, 10.29)
2.
You are given the following for a double decrement table:
(a)
(b)
qx(2) = 0.01
(c)
Each decrement is uniformly distributed over each year of age in its associated
single decrement tabl

1.
DO NOT HAND IN: Text: 11.6, 11.7, 11.8, 11.9
2.
A pension plan provides a death benefit equal to the return of the participant's
contributions with interest at 5%. For (x+h) you are given:
(a)
(AS)x+h = 30,000
(b)
Sy=(1.04)y
(c)
Contributions are made

1.
You are given the following triple decrement probabilities:
Age
q(1)x
q(2)x
q(3)x
x
0.1
0.2
0.2
x+1
0.2
0.3
0.4
x+2
0.3
0.3
0.4
For an initial set of 1000 lives age (x), what are the total expected terminations
by decrement 3 over the next 3 years?
2.