COUNTRY ANALYSIS UNIT
FEDERAL RESERVE BANK OF SAN FRANCISCO
JUNE 2011
Banking Reform in Vietnam
V
ietnams banking sector is expected to have
one of the highest growth rates in Asia during
the next few years due to the countrys continued
economic expansion
19.7. FIXED PENSION SCHEMES
309
(c) A fraction of the final salary per year of service.
Notes
1. Years of service normally include fractions counting pro rata.
2. The benefits on the date of age retirement or ill-health retirement are valued by multiplyin
310
CHAPTER 19. PENSION FUNDS
It follows that
xia =
R
64x
X
1 ia
(t + )Cx+t
2
t=0
Proof.
ia
ia
xia = M
xia + M
x+1
64
R
+ . + M
1
ia
ia
= ( Cxia + Cx+1
+ . + C64
)
2
1 ia
ia
ia
+ ( Cx+1
+ Cx+2
+ . + C64
)
2
+ .
1 ia
+ C64
2
1 ia
1 ia
1
= Cx + 1 Cx+1
320
CHAPTER 19. PENSION FUNDS
Solution
1. Let k be total contribution rate per cent for a new member aged 20. Then
k SAL s
SAL z (i+r)a
i+r ]
N20 =
[ R20
+ 3.z R
20
100 s20 D20
80
s20 D20
Thus
100
k=
80
"
z
i+r
(i+r)a + 3.z R
R
20
20
sN
20
#
= 7.443.
19.11. DEATH AND WITHDRAWAL BENEFITS
19.11
317
Death and Withdrawal Benefits
The benefits on death in service usually consist of one or more of:
1. a fixed sum, or a certain multiple of salary;
2. a return of the employees contributions, accumulated at a
19.8. AVERAGE SALARY SCHEMES
311
Again, this may be separated into the P.S.P. and the F.S.P. terms.
Define the commutations
(
1
v x+ 2 rx a
rx+ 1 , x < 65
ra
2
Cx =
v 65 r65 a
r65
, x = 65
P
65x ra
(note the summation is up to 65 x)
Mxra = t=0 Cx+t
xra =
19.12. RETURN OF CONTRIBUTIONS ON DEATH OR WITHDRAWAL
319
(see the Appendix to this Chapter.)
Note
When j = 0 one may omit the j from the commutation functions, so if contributions are returned
without interest their mean present value is
(T P C)
Mxw
k SA
18.5. SOLUTIONS
299
(b) Let extra premium be E per week.
The equation
of value for E is
K40 K50
(E + 3.25)
= 52.18 0.9E
a40:10
D40
Therefore (E + 3.25) 13.077 = 382.67E
and so
E = 0.115,
say 0.12.
Hence revised premium is 3.37 per week.
18.4
(a) Let weekl
312
CHAPTER 19. PENSION FUNDS
Thus the benefits can be separated into the Past Service Pension and the Future Service Pension.
Value of P.S.P.
1
This is just the value of a fixed pension of 60
(T.P.S.) so, using the functions defined in the
previous secti
314
CHAPTER 19. PENSION FUNDS
Define the commutation functions
z
z
Cxia = zx+ 12 Cxia ,
Mxia =
64x
X
z
C ia
x+t ,
t=0
z
and
z
1 z ia
xia = z M ia
M
C ,
x
2 x
64x
X
ia =
R
x
z
ia
M
x+t =
64x
X
t=0
1
(t + )z C ia
x+t
2
t=0
(note similarity to definition
15.2. THE ASSOCIATED SINGLE-DECREMENT TABLES
15.2
249
The Associated Single-Decrement Tables
Each mode of decrement may be thought of as possessing its own life table, denoted by, for
example, lx or lx . Thus
t px
= P rcfw_(x) does not exit by mode before
19.9. FINAL SALARY SCHEMES
315
Example 19.9.1. Three members of a pension scheme whose age nearest birthday is 45 have the
following annual rates of salary and exact numbers of years of past service:
A : 15,000 20 years
B : 12,000 10 years
C : 14,000 5 ye
19.4. SALARY SCALES
305
Using approximate integration in (19.4.2), we have
sx ' sx+ 12 '
1
[
sx + sx+1 ]
2
(19.4.3)
Formulae and Tables gives values of sx (not sx ), so we find sx by linear interpolation:
sx '
1
[sx1 + sx ] ' sx 12
2
(19.4.4)
Note
To esti
302
CHAPTER 18. SICKNESS FUNCTIONS
next. The experience of occupation group AHJ is given in Tables for Actuarial Examinations.
Since the middle classes and well-to-do did not (in general) join friendly societies providing
sickness benefits, this represent
248
CHAPTER 15. MULTIPLE-DECREMENT TABLES
and
t (aq)x
=P rcfw_T < t
=P rcfw_(x) leaves before time t, either by
mode or mode
t (aq)x
= the probability that (x) gets married
or leaves service (or does both
these things) within t years
In the example above
Chapter 15
MULTIPLE-DECREMENT
TABLES
15.1
Introduction
Consider a body of lives subject to two modes of decrement, and . For example, consider
a group of bachelor employees of a large company, from which men can leave by either mode ,
marriage, or by mode
250
CHAPTER 15. MULTIPLE-DECREMENT TABLES
Put x = x0 , y = x0 + t to obtain
(al)y = k.ly .ly (y x0 )
where k is a constant. If we choose the radix (al)x0 to be equal to lx0 .lx0 , then
(al)y = ly .ly
for all y x0 ( as k = 1)
Some Important Formulae
t (aq)
306
CHAPTER 19. PENSION FUNDS
(iv) Annual salary rate at 64 is 9192 ss64
' 27, 499
25
s64 1
Annual salary rate at 64 21 is 9192 s252 ' 27, 576
Hence by linear extrapolation the annual salary rate at age 65 is approximately
27, 576 + (27, 576 27, 499) = 27
304
CHAPTER 19. PENSION FUNDS
member who has not yet retired).
The reserve for each member is calculated prospectively. That is,
reserve = mean present value of future benefits - mean present
value of future contributions (of both employee and employer)
N
308
CHAPTER 19. PENSION FUNDS
payable continuously. Then the mean present value of future contributions is
Z 65x
lx+t
F
vt
dt
lx
0
64x
X
1 lx+t+ 1
2
'F
v t+ 2
l
x
t=0
=F
64x
X
Dx+t+ 12
t=0
Dx
64x
X
1
x+t
D
Dx t=0
Nx
=F
Dx
'F
(19.5.3)
x = P64x D
x+t .
19.5. THE VALUE OF FUTURE CONTRIBUTIONS
307
R
x = 1 Dx+t dt ' Dx+ 1 ' 1 [Dx + Dx+1 ]
D
2
0
2
s
x
Dx = sx D
and P
64x
s
Nx = t=0 s D
x+t
One can now evaluate (19.5.1) by means of commutation functions, giving a mean present value
of
1
64x x+t+ 2
.lx+t+
19.9. FINAL SALARY SCHEMES
313
has to be added.
On defining the commutation
functions
s ra
xra and s R
xra = P64x s M
ra
Mx = sx M
x+t
t=0
and using a similar argument to that used for ill-health retirements, the value of the F.S.P. is
found to be
SAL
316
CHAPTER 19. PENSION FUNDS
(a) If n < 40, then leave the P.S.P. unchanged but restrict the F.S.P. . In the final salary scheme
mentioned above, the value of the F.S.P. is altered to
SAL z (i+r)a z (i+r)a
Rx
Rx+40n
80
sx Dx
(19.9.5)
(b) If n 40, then
Chapter 19
PENSION FUNDS
19.1
General Introduction
Pension schemes may be described (in broad terms) as either:
(a) defined - benefit schemes,
or
(b) defined - contribution schemes.
Defined - benefit schemes
These are pension schemes whereby the pension a
318
CHAPTER 19. PENSION FUNDS
Example 19.11.1. A company has a pension scheme which provides a pension upon retirement
1
of 80
th of the final salary per year of service. In addition the sum of 10,000 is paid on death in
service of a member. If all contri