People are lost if it comes down to their pension. A recent (2012)
Friends Life survey found that 68% of Britons do not know the collective value of their pension funds.....
This result is in line with a
Dutch 2011 survey, that concludes that 66% has no knowledge of their pension.
Pension illiteracy is clearly a worldwide phenomenon. Pensions are a 'low
interest' product. Unfortunately  nowadays  in the double sense of the
latter words.
As an actuary, people often ask me at a birthday party : I'm paying a 1000 bucks contribution each year for my pension, but does it pay out in the end? Can you tell me?
Unfortunately most actuaries, including myself, answer this question by telling that
this is a difficult question to answer straightforward and that the pension outcome depends on topics like age, mortality, return, inflation, gender, indexation, investment scheme, asset mix, etc., etc.....
Simplifying
To make a breakthrough in this pension communication paradox, let's try to create more pension insight with a simple approach. But remember  as with everything in life  the word 'simple' implies that we can not be complete as well as consistent at the same time. After all,
Kurt Gödel's incompleteness theorems clearly show that nothing in life can be both complete and consistent at the same time.
Thanks to God and Gödel, we can stay alive on this planet by simplifying everything in life to a level that our brains can comprise. We'll keep it that way in this blog as well.
How much pension Benefits for how much contribution?
First thing to do, is to give the average low pension interested person on this planet an overall hunch on what a yearly investment of a 1000 bucks(first simplification: S1)until the pension age of 65 year (S2) delivers in terms of a yearly pension as of age 65 in case of an average pension fund.
If we state 'bucks' here, we mean your local general currency. We denote 'bucks' here simply as $, or leave it out. So $ stands for €, ¥ , £ or even $ itself.
Now let's calculate for different pension contribution start ages (S3)what a yearly contribution of $ 1000 (payable in months at the beginning of each month; S4), pays back in terms of a yearly pension (payable in months at the end of each month; S5) on basis of a set of different constant return rates (S6). The calculation is on a net basis (so without costs; S7), a Dutch (2008) mortality table (S8) and without any
inflation (S9), any pension indexation (S10), any contribution indexation (S11), or any tax influence (S12).
Here's the simple table we're looking for:
TABLE 1
Yearly Pension at age 65 on basis of 1000 yearly contribution 
Pension Indexation=0%, Contribution Indexation=0%, Inflation: 0% 
Start  Net Yearly Return Rate 
Age  0%  1%  2%  3%  4%  5%  6%  7%  8% 
25  2692  3669  5019  6898  9521  13192  18336  25553  35681 
30  2345  3113  4134  5503  7342  9812  13133  17601  23612 
35  1999  2584  3335  4304  5555  7171  9257  11949  15421 
40  1654  2084  2614  3273  4092  5109  6370  7933  9867 
45  1311  1610  1964  2388  2896  3502  4225  5085  6107 
50  972  1163  1380  1632  1921  2254  2635  3072  3570 
55  638  744  860  989  1132  1291  1465  1657  1868 
60  312  355  400  448  499  554  612  674  738 
In a graphical view on a logarithmic pension benefits scale, it looks something like this:
Example
To illustrate what is happening, a simple example:
When you join your pension fund at age 40 and start saving $ 1000 a year (the first of every month: $ 83.33) until your 65, you'll receive a yearly pension benefit of $ 4092 yearly ( $ 341 at the end of every month) from age 65 of, as long as you live.
From this table, we can already draw some very basic conclusions:
 To build up a substantial pension, it pays out if you start early in life
 The pension outcome is heavily dependent on the yearly return of your pension fund
 Most pension funds operate on basis of a 'general employee and/or employer
contribution' instead of individual employee contributions.
This implies that younger employees pay more than they should have paid on an individual basis and older employees less. In other words, younger employees subsidize older employees. How much more, you can derive from the tables above and by comparing the individual
contributions to the general contribution level of the pension fund.
Pension Indexation
As we all want to protect our pension against inflation, let's calculate
the outcome of a 'real pension' instead of a 'nominal pension'. As long
term yearly inflation rates vary between 2% and 3%, we make the same
calculation as above, but now the yearly pension outcome (as from age
65) will be indexed with 3% (fixed) at the end of every year and the
yearly contribution paid, will also be yearly indexed with 3%.
Here's the outcome:
TABLE 2
Yearly Pension at age 65 on basis of 1000 yearly contribution 
Pension Indexation=3%, Contribution Indexation=3%, Inflation: 0% 
Start  Net Yearly Return Rate 
Age  0%  1%  2%  3%  4%  5%  6%  7%  8% 
25  3687  4914  6566  8814  11889  16112  21933  29978  41124 
30  2947  3859  5051  6624  8707  11468  15138  20021  26526 
35  2309  2968  3803  4872  6241  7994  10240  13119  16809 
40  1760  2218  2781  3479  4344  5413  6735  8368  10382 
45  1288  1590  1949  2381  2897  3515  4251  5127  6168 
50  882  1066  1277  1523  1807  2134  2512  2944  3440 
55  536  633  741  862  998  1149  1316  1502  1706 
60  243  281  321  364  411  461  515  573  634 
To get grip at the comparison between a real and a nominal pension, we
express the real pension (3% Indexed Pensions and Contribution) as a
percentage of the nominal pension:
TABLE 3
Yearly Pension at age 65 on basis of 1000 yearly contribution 
'3% P&CIndexed Pensions' as percentage '0% P&CIndexed Pensions' 
Start  Net Yearly Return Rate 
Age  0%  1%  2%  3%  4%  5%  6%  7%  8% 
25  137%  134%  131%  128%  125%  122%  120%  117%  115% 
30  126%  124%  122%  120%  119%  117%  115%  114%  112% 
35  116%  115%  114%  113%  112%  111%  111%  110%  109% 
40  106%  106%  106%  106%  106%  106%  106%  105%  105% 
45  98%  99%  99%  100%  100%  100%  101%  101%  101% 
50  91%  92%  93%  93%  94%  95%  95%  96%  96% 
55  84%  85%  86%  87%  88%  89%  90%  91%  91% 
60  78%  79%  80%  81%  82%  83%  84%  85%  86% 
From this last table we can conclude that if you start saving for your pension below the age of 40 your indexed savings weight up to the indexed pension. Above the age of 45 it is the other way around.
The above figures are the kind of figures (magnitude) you'll find on your
benefits statements. You can compare in practice whether your benefit
statement is in line with the above tables....
The Inflation Monster
In the last given example, pension is 3% inflation protected as from the moment of retirement.
However, if pension is not also yearly fully indexed (in this case: 3%) during
the contribution period, there still is a major potential inflation erosion risk left.
In this case it's interesting to examine what the value of a 3% indexed
pension in combination with a 3% indexed contribution is worth in terms
of actual money, as inflation would continue at a constant 3% level each year. Here's the answer:
TABLE 4
Yearly Pension at age 65 on basis of 1000 yearly contribution 
Pension Indexation=3%, Contribution Indexation=3%, Inflation: 3% 
Start  Net Yearly Return Rate 
Age  0%  1%  2%  3%  4%  5%  6%  7%  8% 
25  1130  1507  2013  2702  3645  4939  6724  9190  12607 
30  1047  1371  1795  2354  3094  4076  5380  7115  9427 
35  951  1223  1567  2007  2571  3293  4219  5405  6925 
40  841  1059  1328  1662  2075  2586  3217  3997  4959 
45  713  880  1079  1318  1604  1946  2354  2839  3415 
50  566  684  820  977  1160  1370  1612  1890  2208 
55  399  471  552  642  742  855  979  1117  1269 
60  210  242  277  314  355  398  445  494  547 
What we notice is a substantial inflation erosion effect as the pension fund participants get younger.
Let's zoom in on an example to see what we can achieve with these tables.
Example
 From table 2 we can conclude that  at a 4% return rate  a 40 year
old starting pension fund member, with a $ 1000 dollar yearly 3% indexed
contribution will reach a 3% yearly indexed pension of $ 4344 yearly at
age 65.
 From table 4 we can subsequently conclude that, based
on an inflation rate of 3%, this $ 4344 pension has a 'real' value of $
2075, if it's expressed in the value money had when the participant was
40 years old (so, at the start).
 From table 4 we can also conclude that in order to 'compensate' inflation erosion for this pension member, the pension fund has to achieve a return of around 7.4%.
This follows from simple linear interpolation:
7,4% = 7% + 1% * (43443997)/(49593997)
I'll leave other examples to your own imagination.
The effect of a constant inflation on a pension is devastating, as the next table shows
TABLE 5
Inflation Erosion 
 Pension indexation=3%
as of age 65
 Contribution indexation=3%
 Inflation=3%

Start
Age  Inflation
Erosion 
25  69% 
30  64% 
35  59% 
40  52% 
45  45% 
50  36% 
55  26% 
60  14% 

From table 5 it becomes clear that Inflation erosion is indeed substantial.
If you have a fully indexed pension from age 65 (who has?) of and you're N years away from your retirement, an inflation of i% will erode your pension with E%. In formula:
Example
Set inflation to 3%. If you're 40 years old and about to retire at 65, you've got 25 years (N=25=6540) ahead of you.
If your pension of let's say $ 10,000 a year is not indexed during this
period, you can buy with this $ 10,000 no more than you could buy today
with $ 4,800.

Your pension is eroded due to inflation with 52% = 1 1.03^25. So only 48% is left.....
Finally
I trust these tables and examples contribute a little to your pension
insight. Just dive into your pension, it's financially relevant and
certainly will pay out!
Remember that all results and examples in this blog are approximations and simplifications on a net base (no costs or taxes are included). In practice pension funds or insurers have tot charge costs for administration, asset management, solvency, guarantees, mortality risk, etc. . This implies that in practice the results could differ strongly with the results as shown in this blog. The examples in this blog are therefore for learning and demonstration purposes only.
The above calculations were made in a few minutes with help of the
Excel Pension Calculator that was developed in 2011 and updated in 2012.
With help of this pension planner you can calculate all kind of variations and set different variables, including different mortality tables (or even define your own mortality table).
You can
download the pension calculator for free and make your own pension calculations.
More information about pension calculating with this simple pension calculator at:
Enjoy your pension, beware of inflation....
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