Pension Payment Increase asof January 1 1997

As of January 1 1997 pension payments have been increased by 6.5525%

.

An explanation of how this is arrived at is given below.

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                  Actual
                   Fund
                  return             $1000 invested at the
          year  for year           beginning of 1993 grows to

          1993  21.1404%      1000.00+1000.00x.211404   =$1,211.40   at end of 1993
                                        and then to
          1994  -1.1628%        1211.40+1211.40x-.01162  = $1,197.32   at end of 1994
                                        and then to
          1995  15.8261%       1197.32+1197.32x.158261   =$1,386.81   at end of 1995
                                         and then to
          1996  17.3443%       1386.81+1386.61x.173443  = $1,627.34   at end of 1996
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                                                   TABLE 1

Moving Equivalent Four Year Annualized Rate

Denote by i the moving four year annualized rate. Then i satisfies the equation

                         1000(1+i)^4=1000(1.211404)(1-.011628)(1.158261)(1.173443).

Solving , we obtain,  i = ((1.211404)(1-.011628)(1.158261)(1.173443))^.25 - 1
   =0.129456. Hence

The Moving Equivalent Four Year Annualized Rate is 12.9456%


This means that  IF the fund rate was 12.9456% for each of the four years, then
the $1000 would also have grown to $1,627.34
(see table 2)

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                   If
                  Fund
                 return            $1000 invested at the
          year    was              beginning of 1993 grows to

          1993  12.9456%      1000.00+1000.00x.129456 =  $1,129.46   at end of 1993
                                         and then to
          1994  12.9456%       1129.46+1129.46x.129456 =  $1,275.67   at end of 1994
                                          and then to
          1995  12.9456%       1275.67+1275.67x.129456 =  $1,440.82   at end of 1995
                                         and then to
          1996  12.9456%       1440.82+1440.82x.129456 =  $1,627.34   at end of 1996
***********************************************************************************************************************
                                                   TABLE 2

Calculation of Increase to Pension Payments


Suppose that on January 1 1996 the cash value of all of your future pension
payments commencing in 1997 (after the 1996
payments had been made) was $100000. Then

                                                      using              using
                                                     assumed          annualized
                                                     Fund rate of        rate of
                                                     6.00%             12.9456%
                         value on January 1 1996      $100,000.00     $100,000.00
                         value on January 1 1997      $106,000.00     $112,945.60

Denote by R  the % increase of the $106000 to $112,945.60.  Then

                          R = ((112945.60-106000)/106000)x100%
                             =( (.129456-.06)/1.06)x100% =      6.5525%

Accordingly the pension payment increase is 6.5525%

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THE ABOVE IS THE NEW WAY THE INCREASE IS CALCULATED
.
HOW Does this compare with the prior method? see below

Using Method Prior to 1997 Prior to January 1 1997 , in order to determine the increase in pension payments, the "Moving Four Year Average Fund Return" was the simple arithmetic average of the four previous actual returns of the Fund. As of January 1 1997 the "Moving Four Year Average Fund Return" is taken to be the "Moving Equivalent Four Year Annualized Rate". If instead of using the annualized rate of 12.9456% , the old aritmetic mean method was used, then the moving four year average used would have been (21.1404-1.1628+15.8261+17.3443)/4 = 13.2870%.
Then,
                                                         using                   using
                                                        assumed             annualized
                                                        Fund rate of            rate of
                                                          6.00%                13.2870%
                         value on January 1 1996        $100,000.00          $100,000.00
                         value on January 1 1997        $106,000.00          $113,287.00

The increase is  R =((113287-106000)/106000)x100% = ((.13870-.06)/1.06)x100 = 6.8745%.
.