A Stochastic Model
of the Long-Range Financial Status
of the OASDI Program—September 2004

  Contents Prev Next List of Tables List of Figures

V. APPENDICES

D. EQUATION PARAMETER ESTIMATES AND REGRESSION STATISTICS

This appendix contains the parameter values and standard errors for each numbered equation described in chapter II. The parameter values include, where applicable, the estimated autoregressive (AR) and moving average (MA) coefficients. In addition, the assumed annual projected values of each variable from the 2004 Trustees Report alternative II (e.g., FtTR) are presented in a table at the end of this appendix.

The standard errors of each regression were used to generate random variation in each of the variables. The random variation in one variable is usually generated independently of the random variation in another variable. However, the mortality improvement variables, economic variable VAR, and disability variables were each generated in such a way that the random error terms were correlated. For each of these, a Cholesky decomposition was performed on a residual variance-covariance matrix. The correlated random error terms were then obtained by multiplying the lower triangular Cholesky matrix by a vector of standard normal random errors.

Total Fertility Rate

Ft = FtTR + φ1 ft-1 + φ2 ft-2 + φ3 ft-3 + φ4 ft-4 + εt –θ1 εt-1,        0.5 ≤ Ft ≤ 3.4     (1)

Note: The total fertility rate was bounded on this interval because the computer model became unstable if the simulated total fertility rate was less than 0.5. The upper bound was set at 3.4 to preserve the symmetry around the ultimate TR04II value of 1.95.

AR Parameters
 
MA Parameters
 
Process mean over
historical period
φ1 = 1.991694
 
θ1 = 0.665162
 
µ = 2.469526
φ2 = -1.508138
 
φ3 = 0.914735
φ4 = -0.419396
Standard Error
sigma hat sub epsilon = 0.090936

Rate of Decrease in Central Death Rate

MRk, t = MRk, tTR + φkmrk, t-1 + εk, t                              (2)

Group ( k )
Sex
Age
AR Parameter ( φk )
Process mean over
historical period
1
M
Under 1
-0.351201
2.869243
2
F
 
-0.372752
2.842529
3
M
1 to 4
-0.416565
3.501578
4
F
 
-0.427767
3.565887
5
M
5 to 9
-0.227505
2.949994
6
F
 
-0.271437
2.997825
7
M
10 to 14
-0.234871
2.155480
8
F
 
-0.182700
2.320293
9
M
15 to 19
-0.193210
0.906328
10
F
 
-0.168664
1.871810
11
M
20 to 24
-0.175331
0.822418
12
F
 
-0.200078
1.914533
13
M
25 to 29
-0.213296
0.689647
14
F
 
-0.185487
1.657118
15
M
30 to 34
-0.214036
0.882346
16
F
 
-0.221462
1.788244
17
M
35 to 39
-0.213548
1.141628
18
F
 
-0.237834
1.777003
19
M
40 to 44
-0.137733
1.173295
20
F
 
-0.223119
1.681488
21
M
45 to 49
-0.153830
1.058397
22
F
 
-0.253837
1.501890
23
M
50 to 54
-0.082579
0.992394
24
F
 
-0.250153
1.418907
25
M
55 to 59
-0.025914
0.891541
26
F
 
-0.221067
1.234432
27
M
60 to 64
-0.107071
0.783572
28
F
 
-0.340946
1.133483
29
M
65 to 69
-0.217861
0.634373
30
F
 
-0.219608
0.975814
31
M
70 to 74
-0.280665
0.610547
32
F
 
-0.269514
0.978308
33
M
75 to 79
-0.256160
0.552180
34
F
 
-0.280206
0.894627
35
M
80 to 84
-0.331191
0.540486
36
F
 
-0.295512
0.816556
37
M
85 to 89
-0.241108
0.361083
38
F
 
-0.185227
0.580038
39
M
90 to 94
-0.242183
0.274489
40
F
 
-0.207037
0.467668
41
M
95 and Up
-0.158566
0.139841
42
F
 
-0.184255
0.322523

Cholesky Decomposition of Residual Variance-Covariance Matrix

V = LL′    L = [A|B|C]    (L is a 42×42 matrix)

   A =
4.62
0
0
0
0
0
0
0
0
0
0
0
0
0
4.58
1.07
0
0
0
0
0
0
0
0
0
0
0
0
4.50
1.57
6.41
0
0
0
0
0
0
0
0
0
0
0
4.82
2.12
6.61
2.12
0
0
0
0
0
0
0
0
0
0
3.45
1.26
4.79
1.53
3.63
0
0
0
0
0
0
0
0
0
3.82
0.85
6.13
1.90
3.14
3.30
0
0
0
0
0
0
0
0
3.48
0.70
5.14
2.19
3.50
1.33
3.41
0
0
0
0
0
0
0
4.53
1.17
6.53
2.51
4.34
2.71
2.22
3.50
0
0
0
0
0
0
5.06
1.36
8.82
3.80
4.25
1.69
3.76
1.85
4.24
0
0
0
0
0
4.19
1.04
7.47
2.90
3.63
2.02
3.12
2.56
1.90
2.92
0
0
0
0
4.46
2.21
9.39
3.80
4.60
1.71
3.99
1.57
4.46
-0.84
3.49
0
0
0
5.07
1.73
9.02
4.46
4.51
2.66
4.05
2.27
3.36
2.56
0.08
3.12
0
0
5.75
2.49
11.22
5.42
5.59
2.70
4.82
2.51
5.68
0.76
1.61
1.75
3.13
0
5.73
2.47
10.87
5.51
5.31
3.18
4.58
3.06
4.38
2.75
-0.26
3.59
1.61
2.25
5.54
2.37
9.69
4.50
4.59
2.22
4.86
2.42
4.51
0.99
0.89
1.51
2.42
0.56
4.61
1.93
8.22
4.26
3.99
2.32
3.70
2.16
3.17
1.72
0.08
2.13
0.87
1.45
4.06
1.26
5.96
2.36
2.74
0.88
3.18
1.38
2.35
0.74
0.72
0.10
1.50
0.10
3.05
0.96
4.76
2.28
2.24
1.13
2.41
1.20
1.34
1.31
0.49
0.72
0.17
0.70
2.80
0.73
3.13
0.53
1.06
0.13
1.78
0.82
1.01
0.59
0.88
-1.08
0.39
-0.19
2.21
0.31
2.67
0.79
1.03
0.61
1.19
0.97
0.63
0.96
0.79
0.02
-0.30
0.04
2.28
0.11
1.71
-0.11
0.53
-0.02
1.17
0.48
0.47
0.46
0.68
-0.91
0.15
-0.13
1.77
-0.06
1.91
0.04
0.57
0.46
0.93
0.38
0.15
0.70
0.30
-0.06
-0.25
0.16
1.62
-0.15
0.93
-0.37
0.00
-0.41
0.59
0.14
0.17
0.45
0.77
-0.88
-0.09
0.11
1.23
0.16
1.57
-0.09
0.41
0.11
0.70
0.16
-0.10
0.68
0.44
-0.40
-0.23
0.38
1.20
-0.41
0.54
-0.55
0.15
-0.16
0.44
0.01
0.09
0.48
0.87
-1.28
-0.23
0.15
1.02
-0.12
1.02
-0.27
0.01
0.20
0.55
-0.10
-0.40
0.69
0.68
-0.86
-0.42
0.24
0.97
-0.12
0.38
-0.61
-0.06
0.01
0.72
0.17
-0.26
0.26
0.46
-1.11
-0.13
0.27
0.77
-0.07
0.71
-0.38
-0.25
0.21
0.62
0.19
-0.67
0.54
0.37
-0.45
-0.29
0.45
0.99
-0.28
0.47
-0.41
-0.36
0.03
0.40
-0.02
-0.13
0.37
0.51
-1.04
-0.10
0.26
0.74
-0.11
0.66
-0.45
-0.48
0.18
0.51
0.19
-0.62
0.59
0.44
-0.59
-0.35
0.44
0.57
-0.24
0.31
-0.72
-0.22
0.10
0.39
0.11
-0.39
0.53
0.68
-1.01
-0.39
0.08
0.61
-0.12
0.31
-0.56
-0.41
0.28
0.59
0.28
-0.83
0.72
0.67
-0.70
-0.70
0.48
0.76
-0.57
0.41
-0.67
-0.54
-0.12
0.25
-0.09
-0.74
0.40
0.55
-0.86
-0.40
0.43
0.72
-0.46
0.27
-0.58
-0.75
0.07
0.41
-0.13
-0.98
0.42
0.53
-0.72
-0.56
0.62
0.61
-0.41
0.24
-0.76
-0.63
-0.04
0.39
-0.08
-0.75
0.46
0.68
-1.34
-0.79
0.29
0.66
-0.22
0.13
-0.67
-0.80
0.08
0.40
-0.26
-0.91
0.53
0.78
-1.11
-0.97
0.58
0.35
-0.63
-0.01
-0.76
-0.69
0.36
0.54
0.08
-1.00
0.77
0.50
-0.79
-0.90
0.64
0.50
-0.58
-0.19
-0.75
-0.63
0.37
0.56
-0.04
-1.04
0.68
0.52
-0.95
-1.04
0.85
0.42
-0.54
-0.07
-0.86
-0.71
0.59
0.50
0.27
-1.02
0.69
0.49
-0.81
-0.93
0.65
0.53
-0.51
-0.13
-1.00
-0.69
0.57
0.64
-0.07
-1.11
0.78
0.56
-0.92
-1.09
0.80
0.51
-0.29
-0.16
-0.72
-0.86
1.13
0.26
0.40
-0.79
0.52
0.25
-1.00
-1.04
0.76
0.60
-0.36
-0.13
-0.87
-0.84
0.91
0.50
0.14
-1.07
0.62
0.32
-1.14
-1.06
0.87

   B =
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2.30
0
0
0
0
0
0
0
0
0
0
0
0
0
1.08
1.78
0
0
0
0
0
0
0
0
0
0
0
0
1.66
-0.16
2.39
0
0
0
0
0
0
0
0
0
0
0
0.48
0.72
1.46
1.69
0
0
0
0
0
0
0
0
0
0
1.48
-0.11
1.96
0.44
1.96
0
0
0
0
0
0
0
0
0
0.45
0.56
0.99
0.59
1.04
1.48
0
0
0
0
0
0
0
0
0.76
-0.09
1.55
0.49
1.14
0.23
1.51
0
0
0
0
0
0
0
0.20
0.44
0.87
0.45
0.48
0.22
0.68
1.13
0
0
0
0
0
0
0.57
-0.33
1.53
0.51
1.29
0.10
0.63
-0.03
1.54
0
0
0
0
0
0.25
-0.05
0.86
0.61
0.43
0.64
0.17
0.39
0.98
1.18
0
0
0
0
0.67
0.05
0.99
0.47
1.25
0.10
0.84
0.26
0.90
-0.04
1.14
0
0
0
0.39
0.31
0.70
0.91
0.55
0.33
0.53
0.44
0.39
0.23
1.06
1.05
0
0
0.62
-0.27
1.01
0.43
0.75
-0.03
1.11
0.29
1.19
0.03
0.08
-0.11
1.21
0
0.36
0.04
0.76
0.62
0.25
0.29
0.74
0.35
0.67
0.52
0.15
0.24
0.64
0.92
0.33
-0.08
1.08
0.57
1.15
0.22
0.62
0.21
0.96
-0.02
0.55
0.16
0.60
-0.06
0.09
0.52
0.78
0.68
0.56
0.31
0.39
0.14
0.60
0.16
0.65
0.50
0.26
0.26
0.54
-0.06
0.89
0.48
0.75
0.28
0.79
0.22
1.11
0.15
0.50
-0.10
0.97
0.10
0.44
0.30
0.76
0.61
0.36
0.37
0.63
0.29
0.84
0.50
0.61
0.07
0.59
0.38
-0.05
0.25
1.00
0.77
0.51
0.15
0.67
0.23
1.09
0.12
0.89
0.06
0.59
0.41
-0.12
0.64
1.03
1.11
0.47
0.32
0.62
0.22
0.97
0.31
0.88
0.37
0.48
0.54
0.07
0.21
0.90
0.77
0.59
0.54
0.62
0.23
1.24
0.48
0.69
-0.07
0.76
0.52
-0.09
0.47
0.93
0.90
0.62
0.52
0.54
0.11
1.32
0.51
0.76
0.06
0.71
0.77
-0.15
0.38
1.34
0.87
0.16
0.18
0.64
0.41
1.28
0.14
0.87
0.00
1.10
0.64
-0.49
0.52
1.38
1.20
0.21
0.07
0.88
0.13
1.34
0.39
0.83
-0.12
1.02
0.83
-0.22
0.48
1.50
0.91
0.18
0.14
0.51
0.30
1.15
0.22
0.91
0.09
1.13
0.69
-0.57
0.52
1.45
1.01
0.14
0.06
0.77
0.11
1.30
0.39
0.83
-0.09
1.04
0.90
-0.12
0.41
1.98
1.11
0.05
0.12
0.24
0.20
0.82
0.12
1.29
0.30
1.13
0.68
-0.31
0.47
1.72
1.05
0.01
0.09
0.48
-0.08
1.11
0.41
1.07
0.06
1.04
1.08

   C =
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.06
0
0
0
0
0
0
0
0
0
0
0
0
0
0.69
1.13
0
0
0
0
0
0
0
0
0
0
0
0
0.25
-0.01
1.07
0
0
0
0
0
0
0
0
0
0
0
0.08
0.63
0.77
0.70
0
0
0
0
0
0
0
0
0
0
0.38
0.33
0.08
-0.12
1.09
0
0
0
0
0
0
0
0
0
0.30
0.89
0.02
0.43
0.78
0.75
0
0
0
0
0
0
0
0
0.67
0.23
0.58
0.22
0.41
0.05
1.18
0
0
0
0
0
0
0
0.38
0.47
0.71
0.63
0.36
0.35
0.83
0.81
0
0
0
0
0
0
0.62
0.44
0.29
0.21
0.72
0.30
0.55
0.45
1.42
0
0
0
0
0
0.69
1.05
0.33
0.46
0.80
0.34
0.61
0.75
0.96
0.83
0
0
0
0
0.69
0.37
0.20
0.28
0.66
0.31
0.63
0.61
1.48
-0.03
0.54
0
0
0
0.71
1.03
0.23
0.50
0.77
0.36
0.69
0.76
0.94
0.85
0.23
0.34
0
0
0.85
0.41
0.04
0.58
0.44
0.35
0.71
0.89
1.53
-0.24
0.94
0.23
1.23
0
0.84
1.08
0.10
0.63
0.68
0.35
0.77
0.95
1.03
0.80
0.67
0.31
0.57
0.41

Legal Immigration

IMt = IMtTR + φ1imt-1 + φ2imt-2 + φ3imt-3 + φ4imt-4 + εt – θ1εt-1,        0 ≤ IMt ≤ 2×IMtTR     (3)

Note: Because legal immigration is a non-negative quantity, its lower bound was set at zero. The upper limit was chosen to preserve the symmetry around the TR04II value.


AR Parameters
 
MA Parameters
 
Process mean over
historical period
φ1 = 1.079587
 
θ1 = -0.487496
 
µ = 460,545
φ2 = -0.538171
 
φ3 = 0.689674
φ4 = -0.309780
Standard Error
sigma hat sub epsilon = 84,770

Legal Emigration

EMt = EMtTR + φ1emt-1 + φ2emt-2 + φ3emt-3 + φ4emt-4 + εt – θ1εt-1,        0 ≤ EMt ≤ 2×EMtTR     (4)

Note: Because legal emigration is a non-negative quantity, its lower bound was set at zero. The upper limit was chosen to preserve the symmetry around the TR04II value.


AR Parameters
 
MA Parameters
φ1 = 0.269897
 
θ1 = -0.121874
φ2 = -0.134543
 
φ3 = 0.172419
φ4 = -0.077445
Standard Error
sigma hat sub epsilon = 21,192

Net Other Immigration

ΔΟt = ΔΟtTR + εt          Ο2003 = Ο2003TR = 400,000            (5)

Standard Error
sigma hat sub epsilon = 25,371

Economic Variable VAR

Unemployment Rate (expressed as log-odds ratio)

Ut = UtTR + a111ut-1 + a112ut-2 + a121it-1 + a122it-2 + a131rt-1 + a132rt-2 + ε1t      (6)


AR Parameters
 
Process mean over
historical period
a111 = 0.960146
 
a112 = -0.304386
 
µ = -2.796475
a121 = 0.400633
 
a122 = -0.083907
 
a131 = 0.746191
 
a132 = 0.610372

Inflation Rate (transformed into logs with lower bound of -3.0%)

It = ItTR + a211ut-1 + a212ut-2 + a221it-1 + a222it-2 + a231rt-1 + a232rt-2 + ε2t               (7)

AR Parameters
 
Process mean over
historical period
a211 = -0.769000
 
a212 = 0.721055
 
µ = -2.719855
a221 = 0.595616
 
a222 = 0.301637
 
a231 = -4.846046
 
a232 = 1.803246


Real Interest Rate

Rt = RtTR + a311ut-1 + a312ut-2 + a321it-1 + a322it-2 + a331rt-1 + a332rt-2 + ε3t               (8)

Note: The real interest rate was bounded below such that the nominal interest rate would be non-negative.


AR Parameters
 
Process mean over
historical period
a311 = 0.060540
 
a312 = -0.048520
 
µ = 0.030517
a321 = 0.028107
 
a322 = -0.027562
 
a331 = 1.234137
 
a332 = -0.319613


Cholesky Decomposition of Residual Variance-Covariance Matrix

V = LL′    
L =
0.113117
0
0
-0.050445
0.139394
0
0.000952
-0.007164
0.009837


Real Average Wage (percent change)

Wt = WtTR + β2ut + β3ut-1 + εt                             (9)

AR Parameters
 
Process mean over
historical period
β2 = -0.061391
 
µ = 0.012822
β3 = 0.035378
 
Standard Error
sigma hat sub epsilon = 0.011806


Disability Incidence - Male

DIMt = DIMtTR + φ1dimt-1 + φ2dimt-2 + εt                                  (10)

AR Parameters
 
Process mean over
historical period
φ1 = 1.465965
 
µ = 5.559148
φ2 = -0.634930
 


Disability Incidence - Female

DIFt = DIFtTR + φ1dift-1 + φ2dift-2 + εt                                  (11)

AR Parameters
 
Process mean over
historical period
φ1 = 1.447164
 
µ = 4.53556
φ2 = -0.618748
 



Cholesky Decomposition of Residual Variance-Covariance Matrix

V = LL′    
L =
0.369409
0
0.310160
0.198227



Disability Recovery - Male

DRMt = DRMtTR + φ1drmt-1 + εt                                  (12)

AR Parameters
 
Process mean over
historical period
φ1 = 0.577874
 
µ = 10.51046


Disability Recovery - Female

DRFt = DRFtTR + φ1drft-1 + εt                                  (13)

AR Parameters
 
Process mean over
historical period
φ1 = 0.569980
 
µ = 9.590448



Cholesky Decomposition of Residual Variance-Covariance Matrix

V = LL′    
L =
1.697850
0
1.538223
0.470810


Equation Parameters from the 2004 Trustees Report Assumptions
t
FtTR
MR1, tTR
MR2, tTR
MR3, tTR
MR4, tTR
MR5, tTR
MR6, tTR
MR7, tTR
MR8, tTR
2004
2.0167
2.9097
2.7474
3.1458
2.9534
3.0533
2.5483
1.8772
1.4612
2005
2.0139
2.6733
2.5448
2.7958
2.6463
2.7069
2.3225
1.7531
1.4460
2006
2.0112
2.4845
2.3829
2.5161
2.4008
2.4350
2.1433
1.6580
1.4344
2007
2.0084
2.3338
2.2535
2.2923
2.2041
2.2203
2.0006
1.5840
1.4253
2008
2.0056
2.2133
2.1500
2.1128
2.0464
2.0501
1.8865
1.5260
1.4178
2009
2.0028
2.1170
2.0672
1.9688
1.9197
1.9145
1.7949
1.4800
1.4114
2010
2.0000
2.0399
2.0009
1.8530
1.8178
1.8062
1.7213
1.4432
1.4058
2011
1.9973
1.9781
1.9478
1.7598
1.7356
1.7194
1.6619
1.4134
1.4007
2012
1.9945
1.9287
1.9051
1.6846
1.6693
1.6495
1.6137
1.3892
1.3960
2013
1.9917
1.8889
1.8709
1.6239
1.6156
1.5931
1.5746
1.3692
1.3917
2014
1.9889
1.8571
1.8434
1.5746
1.5721
1.5474
1.5427
1.3528
1.3875
2015
1.9861
1.8314
1.8213
1.5347
1.5366
1.5103
1.5165
1.3390
1.3836
2016
1.9833
1.8107
1.8034
1.5021
1.5076
1.4800
1.4950
1.3273
1.3798
2017
1.9806
1.7940
1.7890
1.4754
1.4839
1.4552
1.4772
1.3174
1.3762
2018
1.9778
1.7805
1.7773
1.4535
1.4643
1.4347
1.4623
1.3089
1.3727
2019
1.9750
1.7695
1.7677
1.4354
1.4480
1.4177
1.4498
1.3015
1.3693
2020
1.9723
1.7605
1.7599
1.4203
1.4344
1.4035
1.4392
1.2950
1.3660
2021
1.9695
1.7532
1.7535
1.4077
1.4229
1.3916
1.4301
1.2893
1.3627
2022
1.9667
1.7471
1.7483
1.3970
1.4132
1.3815
1.4223
1.2841
1.3596
2023
1.9639
1.7421
1.7439
1.3879
1.4049
1.3728
1.4155
1.2794
1.3564
2024
1.9611
1.7379
1.7402
1.3801
1.3976
1.3653
1.4094
1.2751
1.3534
2025
1.9584
1.7344
1.7371
1.3733
1.3912
1.3587
1.4041
1.2712
1.3503
2026
1.9556
1.7314
1.7344
1.3673
1.3856
1.3529
1.3992
1.2675
1.3473
2027
1.9528
1.7288
1.7321
1.3619
1.3805
1.3477
1.3947
1.2639
1.3444
2028
1.9500
1.7212
1.7255
1.3486
1.3684
1.3348
1.3849
1.2576
1.3408
2029
1.9500
1.7203
1.7247
1.3458
1.3656
1.3321
1.3822
1.2549
1.3380
2030
1.9500
1.7193
1.7238
1.3431
1.3629
1.3294
1.3794
1.2523
1.3352
2031
1.9500
1.7184
1.7229
1.3404
1.3601
1.3266
1.3766
1.2497
1.3324
2032
1.9500
1.7175
1.7220
1.3377
1.3573
1.3239
1.3738
1.2471
1.3296
2033
1.9500
1.7165
1.7212
1.3350
1.3546
1.3212
1.3711
1.2445
1.3268
2034
1.9500
1.7156
1.7203
1.3323
1.3518
1.3185
1.3683
1.2419
1.3240
2035
1.9500
1.7146
1.7194
1.3296
1.3491
1.3158
1.3656
1.2394
1.3213
2036
1.9500
1.7137
1.7185
1.3270
1.3464
1.3131
1.3628
1.2368
1.3185
2037
1.9500
1.7127
1.7176
1.3243
1.3436
1.3105
1.3601
1.2343
1.3157
2038
1.9500
1.7117
1.7167
1.3216
1.3409
1.3078
1.3573
1.2317
1.3130
2039
1.9500
1.7108
1.7158
1.3190
1.3382
1.3051
1.3546
1.2292
1.3103
2040
1.9500
1.7098
1.7149
1.3163
1.3355
1.3025
1.3519
1.2267
1.3075
2041
1.9500
1.7088
1.7139
1.3137
1.3328
1.2998
1.3491
1.2242
1.3048
2042
1.9500
1.7078
1.7130
1.3110
1.3301
1.2972
1.3464
1.2217
1.3021
2043
1.9500
1.7068
1.7121
1.3084
1.3274
1.2946
1.3437
1.2193
1.2994
2044
1.9500
1.7058
1.7111
1.3058
1.3247
1.2920
1.3410
1.2168
1.2967
2045
1.9500
1.7048
1.7102
1.3032
1.3220
1.2893
1.3383
1.2144
1.2940
2046
1.9500
1.7038
1.7092
1.3006
1.3194
1.2868
1.3357
1.2120
1.2913
2047
1.9500
1.7027
1.7083
1.2980
1.3167
1.2841
1.3330
1.2095
1.2887
2048
1.9500
1.7017
1.7073
1.2954
1.3141
1.2816
1.3303
1.2071
1.2860
2049
1.9500
1.7007
1.7063
1.2929
1.3114
1.2790
1.3276
1.2047
1.2834
2050
1.9500
1.6996
1.7054
1.2903
1.3088
1.2764
1.3250
1.2024
1.2807
2051
1.9500
1.6986
1.7044
1.2877
1.3062
1.2739
1.3223
1.2000
1.2781
2052
1.9500
1.6975
1.7034
1.2852
1.3035
1.2713
1.3197
1.1977
1.2755
2053
1.9500
1.6965
1.7024
1.2826
1.3009
1.2688
1.3170
1.1953
1.2729
2054
1.9500
1.6954
1.7014
1.2801
1.2983
1.2663
1.3144
1.1930
1.2703
2055
1.9500
1.6943
1.7004
1.2776
1.2957
1.2637
1.3118
1.1907
1.2677
2056
1.9500
1.6932
1.6994
1.2751
1.2931
1.2612
1.3091
1.1884
1.2651
2057
1.9500
1.6921
1.6984
1.2726
1.2905
1.2587
1.3065
1.1861
1.2625
2058
1.9500
1.6910
1.6973
1.2701
1.2880
1.2563
1.3039
1.1838
1.2600
2059
1.9500
1.6899
1.6963
1.2676
1.2854
1.2538
1.3013
1.1816
1.2574
2060
1.9500
1.6888
1.6953
1.2651
1.2828
1.2513
1.2987
1.1793
1.2549
2061
1.9500
1.6877
1.6942
1.2627
1.2803
1.2488
1.2962
1.1771
1.2524
2062
1.9500
1.6866
1.6932
1.2602
1.2777
1.2464
1.2936
1.1749
1.2498
2063
1.9500
1.6855
1.6921
1.2578
1.2752
1.2440
1.2910
1.1727
1.2473
2064
1.9500
1.6843
1.6910
1.2553
1.2727
1.2415
1.2885
1.1704
1.2448
2065
1.9500
1.6832
1.6900
1.2529
1.2702
1.2391
1.2859
1.1683
1.2423
2066
1.9500
1.6820
1.6889
1.2505
1.2677
1.2367
1.2834
1.1661
1.2399
2067
1.9500
1.6809
1.6878
1.2481
1.2652
1.2343
1.2809
1.1639
1.2374
2068
1.9500
1.6797
1.6867
1.2457
1.2627
1.2319
1.2784
1.1618
1.2349
2069
1.9500
1.6785
1.6856
1.2433
1.2602
1.2295
1.2758
1.1597
1.2325
2070
1.9500
1.6773
1.6845
1.2409
1.2578
1.2272
1.2733
1.1575
1.2301
2071
1.9500
1.6762
1.6834
1.2385
1.2553
1.2248
1.2708
1.1554
1.2276
2072
1.9500
1.6750
1.6823
1.2362
1.2528
1.2225
1.2683
1.1533
1.2252
2073
1.9500
1.6738
1.6812
1.2338
1.2504
1.2201
1.2659
1.1513
1.2228
2074
1.9500
1.6726
1.6801
1.2315
1.2480
1.2178
1.2634
1.1492
1.2204
2075
1.9500
1.6713
1.6789
1.2291
1.2455
1.2155
1.2609
1.1471
1.2180
2076
1.9500
1.6701
1.6778
1.2268
1.2431
1.2132
1.2585
1.1451
1.2157
2077
1.9500
1.6689
1.6766
1.2245
1.2407
1.2109
1.2561
1.1431
1.2133
2078
1.9500
1.6676
1.6755
1.2222
1.2383
1.2086
1.2536
1.1411
1.2110
2079
1.9500
1.6664
1.6743
1.2199
1.2360
1.2063
1.2512
1.1390
1.2086

Equation Parameters from the 2004 Trustees Report Assumptions
t
MR9, tTR
MR10, tTR
MR11, tTR
MR12, tTR
MR13, tTR
MR14, tTR
MR15, tTR
MR16, tTR
MR17, tTR
2004
1.2537
1.0197
1.4051
1.1711
1.5643
0.7808
0.5897
0.0972
0.1171
2005
1.1661
0.9759
1.2872
1.0909
1.4114
0.7787
0.6290
0.2320
0.2625
2006
1.0973
0.9413
1.1944
1.0295
1.2938
0.7799
0.6686
0.3430
0.3855
2007
1.0429
0.9139
1.1212
0.9820
1.2027
0.7827
0.7054
0.4335
0.4883
2008
0.9999
0.8920
1.0631
0.9449
1.1316
0.7858
0.7380
0.5070
0.5731
2009
0.9656
0.8744
1.0169
0.9156
1.0757
0.7887
0.7660
0.5661
0.6425
2010
0.9382
0.8602
0.9800
0.8923
1.0316
0.7910
0.7895
0.6135
0.6989
2011
0.9162
0.8486
0.9504
0.8736
0.9965
0.7928
0.8088
0.6513
0.7443
2012
0.8986
0.8391
0.9267
0.8585
0.9685
0.7940
0.8244
0.6812
0.7807
2013
0.8843
0.8313
0.9076
0.8462
0.9460
0.7947
0.8369
0.7048
0.8097
2014
0.8728
0.8248
0.8922
0.8361
0.9278
0.7949
0.8468
0.7232
0.8326
2015
0.8634
0.8193
0.8797
0.8277
0.9131
0.7947
0.8545
0.7376
0.8507
2016
0.8557
0.8148
0.8695
0.8207
0.9011
0.7941
0.8603
0.7486
0.8647
2017
0.8495
0.8109
0.8612
0.8148
0.8912
0.7933
0.8647
0.7570
0.8755
2018
0.8443
0.8076
0.8544
0.8098
0.8831
0.7922
0.8679
0.7633
0.8837
2019
0.8400
0.8047
0.8489
0.8055
0.8764
0.7910
0.8700
0.7679
0.8898
2020
0.8365
0.8022
0.8442
0.8017
0.8708
0.7896
0.8715
0.7712
0.8943
2021
0.8335
0.8000
0.8404
0.7984
0.8660
0.7882
0.8723
0.7733
0.8974
2022
0.8309
0.7980
0.8371
0.7955
0.8620
0.7867
0.8726
0.7746
0.8994
2023
0.8288
0.7962
0.8344
0.7929
0.8585
0.7851
0.8725
0.7753
0.9006
2024
0.8269
0.7946
0.8320
0.7905
0.8555
0.7834
0.8720
0.7754
0.9011
2025
0.8253
0.7931
0.8300
0.7883
0.8528
0.7818
0.8714
0.7750
0.9010
2026
0.8239
0.7918
0.8283
0.7862
0.8505
0.7801
0.8705
0.7744
0.9005
2027
0.8226
0.7905
0.8267
0.7843
0.8484
0.7784
0.8695
0.7734
0.8997
2028
0.8195
0.7881
0.8227
0.7809
0.8435
0.7770
0.8705
0.7759
0.9034
2029
0.8188
0.7872
0.8220
0.7796
0.8423
0.7752
0.8688
0.7738
0.9011
2030
0.8182
0.7863
0.8213
0.7782
0.8412
0.7735
0.8672
0.7718
0.8989
2031
0.8176
0.7854
0.8206
0.7768
0.8401
0.7718
0.8655
0.7699
0.8967
2032
0.8170
0.7844
0.8199
0.7755
0.8390
0.7701
0.8639
0.7679
0.8945
2033
0.8164
0.7835
0.8192
0.7742
0.8379
0.7684
0.8623
0.7660
0.8924
2034
0.8158
0.7827
0.8185
0.7729
0.8368
0.7667
0.8608
0.7641
0.8903
2035
0.8151
0.7818
0.8179
0.7716
0.8358
0.7651
0.8592
0.7622
0.8882
2036
0.8146
0.7809
0.8172
0.7703
0.8347
0.7635
0.8577
0.7603
0.8861
2037
0.8140
0.7800
0.8166
0.7690
0.8337
0.7619
0.8562
0.7585
0.8840
2038
0.8134
0.7792
0.8160
0.7678
0.8326
0.7603
0.8547
0.7567
0.8820
2039
0.8129
0.7784
0.8153
0.7665
0.8316
0.7587
0.8532
0.7549
0.8800
2040
0.8123
0.7775
0.8147
0.7653
0.8306
0.7572
0.8517
0.7531
0.8780
2041
0.8118
0.7767
0.8141
0.7641
0.8296
0.7556
0.8503
0.7513
0.8761
2042
0.8112
0.7759
0.8135
0.7628
0.8286
0.7541
0.8488
0.7496
0.8741
2043
0.8107
0.7751
0.8129
0.7617
0.8277
0.7526
0.8474
0.7479
0.8722
2044
0.8101
0.7743
0.8123
0.7605
0.8267
0.7511
0.8460
0.7462
0.8703
2045
0.8096
0.7735
0.8117
0.7593
0.8258
0.7496
0.8446
0.7445
0.8684
2046
0.8091
0.7727
0.8111
0.7582
0.8248
0.7482
0.8432
0.7428
0.8665
2047
0.8086
0.7719
0.8106
0.7570
0.8239
0.7468
0.8419
0.7412
0.8647
2048
0.8081
0.7712
0.8100
0.7559
0.8230
0.7453
0.8406
0.7395
0.8629
2049
0.8076
0.7704
0.8094
0.7548
0.8221
0.7439
0.8392
0.7379
0.8611
2050
0.8071
0.7697
0.8089
0.7537
0.8212
0.7425
0.8379
0.7363
0.8593
2051
0.8066
0.7689
0.8083
0.7526
0.8204
0.7412
0.8366
0.7348
0.8576
2052
0.8061
0.7682
0.8078
0.7515
0.8195
0.7398
0.8354
0.7332
0.8558
2053
0.8056
0.7675
0.8073
0.7505
0.8186
0.7385
0.8341
0.7317
0.8541
2054
0.8052
0.7668
0.8068
0.7494
0.8178
0.7371
0.8329
0.7302
0.8524
2055
0.8047
0.7660
0.8062
0.7484
0.8170
0.7358
0.8316
0.7287
0.8507
2056
0.8043
0.7653
0.8057
0.7473
0.8161
0.7346
0.8304
0.7272
0.8491
2057
0.8038
0.7646
0.8052
0.7463
0.8153
0.7332
0.8292
0.7257
0.8474
2058
0.8034
0.7640
0.8047
0.7453
0.8145
0.7320
0.8280
0.7243
0.8458
2059
0.8029
0.7633
0.8042
0.7443
0.8137
0.7307
0.8268
0.7228
0.8442
2060
0.8025
0.7626
0.8037
0.7433
0.8129
0.7295
0.8257
0.7214
0.8426
2061
0.8020
0.7619
0.8032
0.7423
0.8121
0.7283
0.8245
0.7200
0.8410
2062
0.8016
0.7613
0.8028
0.7414
0.8114
0.7271
0.8234
0.7186
0.8395
2063
0.8012
0.7606
0.8023
0.7404
0.8106
0.7258
0.8223
0.7173
0.8379
2064
0.8008
0.7600
0.8018
0.7395
0.8098
0.7247
0.8211
0.7159
0.8364
2065
0.8004
0.7593
0.8014
0.7385
0.8091
0.7235
0.8201
0.7146
0.8349
2066
0.7999
0.7587
0.8009
0.7376
0.8084
0.7224
0.8190
0.7133
0.8334
2067
0.7995
0.7581
0.8005
0.7367
0.8076
0.7212
0.8179
0.7119
0.8320
2068
0.7991
0.7575
0.8000
0.7358
0.8069
0.7201
0.8168
0.7106
0.8305
2069
0.7987
0.7568
0.7996
0.7349
0.8062
0.7190
0.8158
0.7094
0.8291
2070
0.7984
0.7562
0.7991
0.7340
0.8055
0.7178
0.8147
0.7081
0.8277
2071
0.7980
0.7556
0.7987
0.7331
0.8048
0.7167
0.8137
0.7069
0.8263
2072
0.7976
0.7550
0.7983
0.7323
0.8041
0.7156
0.8127
0.7056
0.8249
2073
0.7972
0.7545
0.7979
0.7314
0.8034
0.7146
0.8117
0.7044
0.8235
2074
0.7968
0.7539
0.7974
0.7305
0.8028
0.7135
0.8107
0.7032
0.8222
2075
0.7965
0.7533
0.7970
0.7297
0.8021
0.7125
0.8097
0.7020
0.8208
2076
0.7961
0.7527
0.7966
0.7289
0.8014
0.7114
0.8088
0.7008
0.8195
2077
0.7958
0.7521
0.7962
0.7281
0.8008
0.7104
0.8078
0.6997
0.8182
2078
0.7954
0.7516
0.7958
0.7272
0.8001
0.7094
0.8069
0.6985
0.8169
2079
0.7950
0.7510
0.7954
0.7264
0.7995
0.7084
0.8059
0.6974
0.8156

Equation Parameters from the 2004 Trustees Report Assumptions
t
MR18, tTR
MR19, tTR
MR20, tTR
MR21, tTR
MR22, tTR
MR23, tTR
MR24, tTR
MR25, tTR
MR26, tTR
2004
-0.0165
0.1965
0.5096
0.9120
1.1420
1.7302
1.3338
1.7585
0.9555
2005
0.1443
0.3353
0.5679
0.9229
1.0793
1.5762
1.2363
1.5985
0.9336
2006
0.2764
0.4528
0.6169
0.9365
1.0300
1.4559
1.1587
1.4721
0.9166
2007
0.3840
0.5509
0.6574
0.9503
0.9909
1.3614
1.0966
1.3718
0.9032
2008
0.4710
0.6318
0.6904
0.9631
0.9596
1.2867
1.0465
1.2918
0.8923
2009
0.5410
0.6979
0.7169
0.9740
0.9342
1.2272
1.0060
1.2278
0.8830
2010
0.5971
0.7515
0.7380
0.9831
0.9134
1.1797
0.9729
1.1762
0.8751
2011
0.6417
0.7946
0.7546
0.9902
0.8963
1.1413
0.9458
1.1345
0.8681
2012
0.6771
0.8290
0.7674
0.9955
0.8820
1.1102
0.9234
1.1006
0.8617
2013
0.7050
0.8563
0.7772
0.9993
0.8699
1.0848
0.9047
1.0728
0.8558
2014
0.7268
0.8778
0.7845
1.0017
0.8596
1.0639
0.8890
1.0498
0.8503
2015
0.7438
0.8945
0.7898
1.0029
0.8507
1.0465
0.8756
1.0307
0.8451
2016
0.7569
0.9074
0.7935
1.0032
0.8429
1.0318
0.8642
1.0146
0.8401
2017
0.7669
0.9171
0.7958
1.0027
0.8360
1.0195
0.8542
1.0010
0.8352
2018
0.7743
0.9243
0.7972
1.0015
0.8298
1.0088
0.8455
0.9893
0.8305
2019
0.7798
0.9295
0.7977
0.9997
0.8243
0.9996
0.8378
0.9791
0.8259
2020
0.7836
0.9331
0.7975
0.9976
0.8191
0.9915
0.8309
0.9702
0.8215
2021
0.7862
0.9354
0.7968
0.9951
0.8144
0.9843
0.8246
0.9622
0.8171
2022
0.7878
0.9366
0.7957
0.9923
0.8100
0.9778
0.8188
0.9551
0.8127
2023
0.7886
0.9370
0.7943
0.9893
0.8058
0.9719
0.8135
0.9486
0.8085
2024
0.7887
0.9368
0.7926
0.9861
0.8018
0.9664
0.8085
0.9425
0.8043
2025
0.7884
0.9360
0.7907
0.9828
0.7980
0.9613
0.8038
0.9369
0.8001
2026
0.7876
0.9347
0.7887
0.9794
0.7944
0.9565
0.7993
0.9316
0.7960
2027
0.7865
0.9332
0.7865
0.9759
0.7908
0.9520
0.7950
0.9266
0.7920
2028
0.7894
0.9362
0.7861
0.9740
0.7863
0.9449
0.7888
0.9189
0.7879
2029
0.7870
0.9332
0.7835
0.9701
0.7832
0.9412
0.7852
0.9148
0.7839
2030
0.7847
0.9303
0.7808
0.9663
0.7801
0.9376
0.7817
0.9108
0.7800
2031
0.7824
0.9275
0.7782
0.9625
0.7771
0.9340
0.7782
0.9069
0.7762
2032
0.7801
0.9246
0.7756
0.9587
0.7741
0.9304
0.7747
0.9029
0.7723
2033
0.7778
0.9218
0.7730
0.9550
0.7711
0.9269
0.7713
0.8990
0.7685
2034
0.7756
0.9190
0.7705
0.9513
0.7682
0.9233
0.7679
0.8951
0.7648
2035
0.7734
0.9162
0.7680
0.9476
0.7653
0.9198
0.7645
0.8912
0.7610
2036
0.7711
0.9135
0.7655
0.9440
0.7624
0.9163
0.7612
0.8873
0.7574
2037
0.7690
0.9108
0.7630
0.9404
0.7596
0.9128
0.7578
0.8835
0.7537
2038
0.7668
0.9081
0.7606
0.9368
0.7568
0.9093
0.7546
0.8797
0.7501
2039
0.7647
0.9054
0.7582
0.9333
0.7540
0.9059
0.7513
0.8759
0.7465
2040
0.7626
0.9028
0.7558
0.9298
0.7513
0.9024
0.7481
0.8721
0.7430
2041
0.7605
0.9002
0.7535
0.9263
0.7485
0.8990
0.7449
0.8684
0.7395
2042
0.7585
0.8976
0.7511
0.9229
0.7459
0.8956
0.7418
0.8646
0.7360
2043
0.7564
0.8951
0.7489
0.9195
0.7432
0.8923
0.7387
0.8610
0.7326
2044
0.7544
0.8925
0.7466
0.9162
0.7406
0.8889
0.7356
0.8573
0.7292
2045
0.7524
0.8900
0.7443
0.9128
0.7380
0.8856
0.7325
0.8536
0.7258
2046
0.7505
0.8876
0.7421
0.9095
0.7354
0.8823
0.7295
0.8500
0.7225
2047
0.7485
0.8851
0.7399
0.9063
0.7329
0.8790
0.7265
0.8464
0.7192
2048
0.7466
0.8827
0.7377
0.9030
0.7304
0.8757
0.7235
0.8428
0.7159
2049
0.7447
0.8803
0.7356
0.8998
0.7279
0.8725
0.7206
0.8392
0.7127
2050
0.7428
0.8779
0.7335
0.8967
0.7254
0.8692
0.7177
0.8357
0.7095
2051
0.7410
0.8756
0.7314
0.8935
0.7230
0.8660
0.7148
0.8322
0.7063
2052
0.7391
0.8733
0.7293
0.8904
0.7206
0.8628
0.7120
0.8287
0.7032
2053
0.7373
0.8710
0.7273
0.8874
0.7183
0.8596
0.7092
0.8253
0.7002
2054
0.7355
0.8687
0.7252
0.8843
0.7159
0.8565
0.7064
0.8218
0.6971
2055
0.7338
0.8665
0.7232
0.8813
0.7136
0.8534
0.7036
0.8184
0.6941
2056
0.7320
0.8643
0.7213
0.8783
0.7113
0.8503
0.7009
0.8150
0.6911
2057
0.7303
0.8621
0.7193
0.8754
0.7091
0.8472
0.6982
0.8116
0.6881
2058
0.7285
0.8599
0.7174
0.8724
0.7068
0.8441
0.6955
0.8083
0.6852
2059
0.7269
0.8578
0.7155
0.8696
0.7046
0.8410
0.6929
0.8050
0.6823
2060
0.7252
0.8556
0.7136
0.8667
0.7025
0.8380
0.6903
0.8017
0.6795
2061
0.7235
0.8535
0.7117
0.8639
0.7003
0.8350
0.6877
0.7984
0.6766
2062
0.7219
0.8515
0.7099
0.8611
0.6982
0.8320
0.6852
0.7952
0.6738
2063
0.7203
0.8494
0.7080
0.8583
0.6961
0.8291
0.6826
0.7920
0.6711
2064
0.7187
0.8474
0.7062
0.8556
0.6940
0.8261
0.6801
0.7887
0.6683
2065
0.7171
0.8453
0.7045
0.8528
0.6920
0.8232
0.6777
0.7856
0.6656
2066
0.7155
0.8434
0.7027
0.8502
0.6899
0.8203
0.6752
0.7824
0.6629
2067
0.7140
0.8414
0.7009
0.8475
0.6879
0.8174
0.6728
0.7793
0.6603
2068
0.7125
0.8395
0.6992
0.8449
0.6860
0.8145
0.6704
0.7762
0.6577
2069
0.7110
0.8375
0.6975
0.8423
0.6840
0.8116
0.6680
0.7731
0.6551
2070
0.7095
0.8356
0.6958
0.8397
0.6821
0.8088
0.6657
0.7700
0.6525
2071
0.7080
0.8337
0.6942
0.8372
0.6802
0.8060
0.6633
0.7670
0.6500
2072
0.7065
0.8319
0.6925
0.8347
0.6783
0.8032
0.6610
0.7640
0.6475
2073
0.7051
0.8300
0.6909
0.8322
0.6764
0.8004
0.6588
0.7610
0.6450
2074
0.7037
0.8282
0.6893
0.8297
0.6746
0.7977
0.6565
0.7580
0.6426
2075
0.7023
0.8264
0.6877
0.8273
0.6728
0.7950
0.6543
0.7551
0.6402
2076
0.7009
0.8246
0.6862
0.8249
0.6710
0.7922
0.6521
0.7522
0.6378
2077
0.6995
0.8229
0.6846
0.8225
0.6692
0.7895
0.6499
0.7493
0.6355
2078
0.6982
0.8211
0.6831
0.8201
0.6674
0.7869
0.6478
0.7464
0.6331
2079
0.6968
0.8194
0.6816
0.8178
0.6657
0.7842
0.6457
0.7436
0.6308

Equation Parameters from the 2004 Trustees Report Assumptions
t
MR27, tTR
MR28, tTR
MR29, tTR
MR30, tTR
MR31, tTR
MR32, tTR
MR33, tTR
MR34, tTR
MR35, tTR
2004
1.5425
0.6333
1.0988
0.1406
1.1434
0.1198
0.9292
0.0663
0.4925
2005
1.4227
0.6763
1.0477
0.2716
1.0847
0.2540
0.9204
0.2200
0.5784
2006
1.3283
0.7123
1.0088
0.3790
1.0397
0.3654
0.9150
0.3476
0.6485
2007
1.2536
0.7417
0.9789
0.4664
1.0047
0.4568
0.9115
0.4523
0.7050
2008
1.1940
0.7654
0.9553
0.5370
0.9772
0.5312
0.9088
0.5376
0.7502
2009
1.1463
0.7842
0.9366
0.5936
0.9551
0.5912
0.9065
0.6065
0.7861
2010
1.1077
0.7989
0.9212
0.6386
0.9371
0.6393
0.9042
0.6616
0.8142
2011
1.0764
0.8100
0.9085
0.6742
0.9222
0.6774
0.9017
0.7054
0.8360
2012
1.0508
0.8182
0.8978
0.7020
0.9097
0.7073
0.8990
0.7399
0.8526
2013
1.0296
0.8241
0.8885
0.7236
0.8990
0.7307
0.8960
0.7667
0.8650
2014
1.0119
0.8280
0.8803
0.7401
0.8896
0.7485
0.8927
0.7873
0.8740
2015
0.9970
0.8302
0.8730
0.7524
0.8812
0.7620
0.8892
0.8028
0.8802
2016
0.9843
0.8312
0.8663
0.7615
0.8738
0.7718
0.8854
0.8142
0.8840
2017
0.9733
0.8312
0.8602
0.7678
0.8669
0.7788
0.8815
0.8223
0.8862
2018
0.9637
0.8303
0.8544
0.7720
0.8605
0.7835
0.8773
0.8277
0.8868
2019
0.9552
0.8287
0.8490
0.7745
0.8545
0.7862
0.8731
0.8310
0.8863
2020
0.9476
0.8266
0.8438
0.7756
0.8488
0.7875
0.8686
0.8324
0.8848
2021
0.9407
0.8240
0.8388
0.7756
0.8433
0.7875
0.8642
0.8325
0.8825
2022
0.9343
0.8211
0.8340
0.7747
0.8381
0.7866
0.8596
0.8315
0.8797
2023
0.9284
0.8180
0.8293
0.7731
0.8330
0.7849
0.8550
0.8296
0.8763
2024
0.9229
0.8146
0.8247
0.7709
0.8281
0.7826
0.8503
0.8270
0.8726
2025
0.9176
0.8111
0.8202
0.7683
0.8232
0.7798
0.8456
0.8238
0.8686
2026
0.9126
0.8074
0.8157
0.7654
0.8185
0.7766
0.8409
0.8201
0.8644
2027
0.9078
0.8037
0.8114
0.7622
0.8138
0.7731
0.8361
0.8161
0.8599
2028
0.9012
0.8018
0.8069
0.7631
0.8089
0.7743
0.8323
0.8176
0.8585
2029
0.8970
0.7976
0.8027
0.7586
0.8045
0.7695
0.8274
0.8120
0.8532
2030
0.8929
0.7934
0.7985
0.7543
0.8001
0.7647
0.8226
0.8065
0.8480
2031
0.8888
0.7893
0.7944
0.7500
0.7957
0.7600
0.8178
0.8011
0.8428
2032
0.8848
0.7852
0.7903
0.7457
0.7913
0.7554
0.8130
0.7957
0.8376
2033
0.8807
0.7811
0.7862
0.7414
0.7870
0.7507
0.8083
0.7903
0.8325
2034
0.8767
0.7771
0.7822
0.7373
0.7827
0.7461
0.8035
0.7850
0.8273
2035
0.8727
0.7732
0.7782
0.7331
0.7785
0.7416
0.7989
0.7798
0.8223
2036
0.8687
0.7692
0.7743
0.7290
0.7743
0.7371
0.7943
0.7746
0.8173
2037
0.8648
0.7654
0.7703
0.7249
0.7701
0.7327
0.7897
0.7694
0.8123
2038
0.8609
0.7615
0.7664
0.7209
0.7659
0.7283
0.7851
0.7643
0.8073
2039
0.8569
0.7577
0.7625
0.7169
0.7618
0.7239
0.7806
0.7592
0.8024
2040
0.8531
0.7539
0.7587
0.7130
0.7577
0.7196
0.7761
0.7542
0.7975
2041
0.8492
0.7502
0.7549
0.7091
0.7537
0.7154
0.7717
0.7493
0.7927
2042
0.8454
0.7465
0.7511
0.7052
0.7497
0.7111
0.7672
0.7444
0.7878
2043
0.8416
0.7428
0.7473
0.7014
0.7457
0.7070
0.7629
0.7395
0.7831
2044
0.8378
0.7392
0.7436
0.6977
0.7417
0.7028
0.7585
0.7347
0.7783
2045
0.8341
0.7356
0.7399
0.6939
0.7378
0.6987
0.7542
0.7299
0.7737
2046
0.8304
0.7321
0.7362
0.6902
0.7339
0.6947
0.7499
0.7252
0.7690
2047
0.8267
0.7285
0.7326
0.6866
0.7301
0.6907
0.7457
0.7205
0.7644
2048
0.8230
0.7251
0.7290
0.6830
0.7263
0.6867
0.7415
0.7159
0.7598
2049
0.8194
0.7216
0.7255
0.6794
0.7225
0.6828
0.7373
0.7113
0.7552
2050
0.8158
0.7182
0.7219
0.6758
0.7187
0.6790
0.7332
0.7068
0.7507
2051
0.8122
0.7149
0.7184
0.6723
0.7150
0.6751
0.7291
0.7023
0.7462
2052
0.8086
0.7115
0.7149
0.6689
0.7113
0.6713
0.7250
0.6979
0.7418
2053
0.8051
0.7082
0.7114
0.6654
0.7076
0.6676
0.7210
0.6935
0.7374
2054
0.8015
0.7050
0.7080
0.6621
0.7040
0.6639
0.7170
0.6892
0.7330
2055
0.7981
0.7018
0.7046
0.6587
0.7004
0.6602
0.7131
0.6849
0.7287
2056
0.7946
0.6985
0.7013
0.6554
0.6969
0.6566
0.7091
0.6807
0.7244
2057
0.7911
0.6954
0.6979
0.6521
0.6933
0.6530
0.7053
0.6764
0.7201
2058
0.7877
0.6923
0.6946
0.6489
0.6898
0.6495
0.7014
0.6723
0.7159
2059
0.7844
0.6892
0.6914
0.6457
0.6864
0.6459
0.6976
0.6682
0.7117
2060
0.7810
0.6861
0.6881
0.6425
0.6830
0.6425
0.6938
0.6641
0.7075
2061
0.7777
0.6831
0.6849
0.6394
0.6796
0.6391
0.6900
0.6601
0.7034
2062
0.7744
0.6802
0.6817
0.6363
0.6762
0.6357
0.6863
0.6561
0.6993
2063
0.7711
0.6772
0.6785
0.6332
0.6728
0.6323
0.6827
0.6522
0.6953
2064
0.7678
0.6743
0.6754
0.6302
0.6695
0.6290
0.6790
0.6483
0.6913
2065
0.7646
0.6714
0.6723
0.6272
0.6662
0.6257
0.6754
0.6445
0.6873
2066
0.7614
0.6686
0.6692
0.6242
0.6630
0.6225
0.6718
0.6407
0.6834
2067
0.7582
0.6657
0.6662
0.6213
0.6598
0.6193
0.6683
0.6369
0.6795
2068
0.7550
0.6629
0.6632
0.6184
0.6566
0.6161
0.6647
0.6332
0.6756
2069
0.7519
0.6602
0.6602
0.6155
0.6534
0.6130
0.6613
0.6295
0.6718
2070
0.7488
0.6574
0.6572
0.6127
0.6503
0.6099
0.6578
0.6259
0.6680
2071
0.7457
0.6548
0.6543
0.6099
0.6472
0.6069
0.6544
0.6223
0.6642
2072
0.7427
0.6521
0.6513
0.6072
0.6441
0.6039
0.6510
0.6187
0.6605
2073
0.7396
0.6495
0.6485
0.6044
0.6411
0.6009
0.6477
0.6152
0.6568
2074
0.7366
0.6469
0.6456
0.6017
0.6381
0.5979
0.6443
0.6118
0.6531
2075
0.7336
0.6443
0.6428
0.5991
0.6351
0.5950
0.6410
0.6083
0.6495
2076
0.7307
0.6418
0.6400
0.5964
0.6322
0.5921
0.6378
0.6049
0.6459
2077
0.7278
0.6392
0.6372
0.5938
0.6292
0.5893
0.6346
0.6016
0.6424
2078
0.7249
0.6368
0.6345
0.5913
0.6263
0.5865
0.6314
0.5983
0.6389
2079
0.7220
0.6343
0.6317
0.5887
0.6235
0.5837
0.6282
0.5950
0.6354

Equation Parameters from the 2004 Trustees Report Assumptions
t
MR36, tTR
MR37, tTR
MR38, tTR
MR39, tTR
MR40, tTR
MR41, tTR
MR42, tTR
IMtTR
EMtTR
2004
-0.0041
0.0426
-0.0753
-0.4091
-0.4196
-1.4868
-1.3316
1,033,333
258,333
2005
0.1766
0.1738
0.0691
-0.1827
-0.2000
-1.0437
-0.9210
1,000,000
250,000
2006
0.3255
0.2810
0.1901
0.0006
-0.0190
-0.6872
-0.5883
966,667
241,667
2007
0.4473
0.3681
0.2905
0.1485
0.1293
-0.4008
-0.3196
933,333
233,333
2008
0.5460
0.4385
0.3728
0.2675
0.2500
-0.1711
-0.1031
900,000
225,000
2009
0.6255
0.4952
0.4400
0.3629
0.3478
0.0130
0.0709
866,667
216,667
2010
0.6891
0.5405
0.4944
0.4393
0.4267
0.1602
0.2106
833,333
208,333
2011
0.7395
0.5767
0.5382
0.5002
0.4900
0.2778
0.3223
800,000
200,000
2012
0.7792
0.6053
0.5732
0.5486
0.5407
0.3715
0.4116
800,000
200,000
2013
0.8100
0.6278
0.6011
0.5869
0.5810
0.4461
0.4828
800,000
200,000
2014
0.8337
0.6453
0.6230
0.6170
0.6129
0.5052
0.5393
800,000
200,000
2015
0.8516
0.6589
0.6401
0.6406
0.6380
0.5521
0.5840
800,000
200,000
2016
0.8648
0.6692
0.6533
0.6590
0.6575
0.5890
0.6193
800,000
200,000
2017
0.8742
0.6770
0.6633
0.6731
0.6726
0.6179
0.6469
800,000
200,000
2018
0.8804
0.6826
0.6708
0.6838
0.6841
0.6405
0.6685
800,000
200,000
2019
0.8843
0.6865
0.6762
0.6918
0.6928
0.6579
0.6851
800,000
200,000
2020
0.8861
0.6891
0.6800
0.6976
0.6990
0.6712
0.6978
800,000
200,000
2021
0.8863
0.6906
0.6823
0.7016
0.7034
0.6813
0.7073
800,000
200,000
2022
0.8852
0.6912
0.6836
0.7042
0.7063
0.6887
0.7142
800,000
200,000
2023
0.8831
0.6911
0.6841
0.7056
0.7080
0.6940
0.7192
800,000
200,000
2024
0.8802
0.6904
0.6838
0.7062
0.7087
0.6976
0.7224
800,000
200,000
2025
0.8767
0.6893
0.6829
0.7060
0.7086
0.6999
0.7244
800,000
200,000
2026
0.8726
0.6878
0.6816
0.7053
0.7078
0.7010
0.7254
800,000
200,000
2027
0.8681
0.6861
0.6799
0.7040
0.7066
0.7014
0.7255
800,000
200,000
2028
0.8698
0.6882
0.6833
0.7089
0.7121
0.7126
0.7362
800,000
200,000
2029
0.8635
0.6853
0.6801
0.7057
0.7088
0.7093
0.7329
800,000
200,000
2030
0.8573
0.6823
0.6769
0.7026
0.7055
0.7062
0.7296
800,000
200,000
2031
0.8511
0.6793
0.6737
0.6995
0.7022
0.7030
0.7262
800,000
200,000
2032
0.8450
0.6764
0.6705
0.6964
0.6989
0.6998
0.7229
800,000
200,000
2033
0.8390
0.6735
0.6673
0.6933
0.6956
0.6966
0.7196
800,000
200,000
2034
0.8329
0.6706
0.6642
0.6903
0.6923
0.6935
0.7163
800,000
200,000
2035
0.8269
0.6677
0.6611
0.6872
0.6891
0.6903
0.7131
800,000
200,000
2036
0.8210
0.6648
0.6579
0.6842
0.6858
0.6872
0.7098
800,000
200,000
2037
0.8152
0.6619
0.6548
0.6811
0.6826
0.6841
0.7065
800,000
200,000
2038
0.8093
0.6591
0.6517
0.6781
0.6794
0.6810
0.7033
800,000
200,000
2039
0.8036
0.6562
0.6486
0.6751
0.6762
0.6779
0.7000
800,000
200,000
2040
0.7979
0.6534
0.6456
0.6721
0.6729
0.6748
0.6968
800,000
200,000
2041
0.7922
0.6506
0.6425
0.6691
0.6697
0.6718
0.6936
800,000
200,000
2042
0.7866
0.6477
0.6395
0.6661
0.6666
0.6687
0.6904
800,000
200,000
2043
0.7810
0.6450
0.6364
0.6632
0.6634
0.6657
0.6871
800,000
200,000
2044
0.7755
0.6422
0.6334
0.6602
0.6603
0.6627
0.6839
800,000
200,000
2045
0.7700
0.6394
0.6304
0.6573
0.6571
0.6596
0.6808
800,000
200,000
2046
0.7646
0.6367
0.6274
0.6544
0.6540
0.6566
0.6776
800,000
200,000
2047
0.7593
0.6339
0.6245
0.6515
0.6509
0.6536
0.6744
800,000
200,000
2048
0.7539
0.6312
0.6215
0.6486
0.6478
0.6507
0.6713
800,000
200,000
2049
0.7487
0.6285
0.6185
0.6457
0.6447
0.6477
0.6681
800,000
200,000
2050
0.7435
0.6258
0.6156
0.6428
0.6416
0.6447
0.6650
800,000
200,000
2051
0.7383
0.6231
0.6127
0.6400
0.6385
0.6418
0.6619
800,000
200,000
2052
0.7332
0.6204
0.6098
0.6371
0.6355
0.6389
0.6588
800,000
200,000
2053
0.7281
0.6178
0.6069
0.6343
0.6324
0.6360
0.6557
800,000
200,000
2054
0.7231
0.6151
0.6040
0.6315
0.6294
0.6331
0.6526
800,000
200,000
2055
0.7182
0.6125
0.6011
0.6287
0.6264
0.6302
0.6495
800,000
200,000
2056
0.7133
0.6099
0.5983
0.6259
0.6234
0.6273
0.6464
800,000
200,000
2057
0.7084
0.6073
0.5954
0.6231
0.6204
0.6244
0.6434
800,000
200,000
2058
0.7036
0.6047
0.5926
0.6204
0.6174
0.6216
0.6403
800,000
200,000
2059
0.6988
0.6021
0.5898
0.6176
0.6145
0.6187
0.6373
800,000
200,000
2060
0.6941
0.5996
0.5870
0.6149
0.6115
0.6159
0.6343
800,000
200,000
2061
0.6895
0.5970
0.5842
0.6122
0.6086
0.6131
0.6313
800,000
200,000
2062
0.6848
0.5945
0.5815
0.6095
0.6057
0.6103
0.6283
800,000
200,000
2063
0.6803
0.5920
0.5787
0.6068
0.6028
0.6075
0.6253
800,000
200,000
2064
0.6757
0.5895
0.5760
0.6041
0.5999
0.6048
0.6223
800,000
200,000
2065
0.6713
0.5870
0.5733
0.6015
0.5970
0.6020
0.6194
800,000
200,000
2066
0.6668
0.5845
0.5705
0.5988
0.5941
0.5993
0.6164
800,000
200,000
2067
0.6625
0.5820
0.5679
0.5962
0.5913
0.5965
0.6135
800,000
200,000
2068
0.6581
0.5796
0.5652
0.5935
0.5884
0.5938
0.6106
800,000
200,000
2069
0.6538
0.5772
0.5625
0.5909
0.5856
0.5911
0.6077
800,000
200,000
2070
0.6496
0.5747
0.5599
0.5884
0.5828
0.5884
0.6048
800,000
200,000
2071
0.6454
0.5723
0.5572
0.5858
0.5800
0.5858
0.6019
800,000
200,000
2072
0.6413
0.5699
0.5546
0.5832
0.5772
0.5831
0.5990
800,000
200,000
2073
0.6372
0.5675
0.5520
0.5806
0.5745
0.5805
0.5962
800,000
200,000
2074
0.6331
0.5652
0.5494
0.5781
0.5717
0.5778
0.5933
800,000
200,000
2075
0.6291
0.5628
0.5468
0.5756
0.5690
0.5752
0.5905
800,000
200,000
2076
0.6252
0.5605
0.5443
0.5731
0.5662
0.5726
0.5877
800,000
200,000
2077
0.6212
0.5581
0.5417
0.5706
0.5635
0.5700
0.5849
800,000
200,000
2078
0.6174
0.5558
0.5392
0.5681
0.5608
0.5674
0.5821
800,000
200,000
2079
0.6135
0.5535
0.5367
0.5656
0.5582
0.5649
0.5793
800,000
200,000

Equation Parameters from the 2004 Trustees Report Assumptions
t
ΔΟtTR
UtTR
ItTR
RtTR
WtTR
DIMtTR
DIFtTR
DRMtTR
DRFtTR
2004
0
-2.8137
-3.1669
0.0323
0.0238
5.2575
5.2156
14.0153
11.7905
2005
0
-2.8354
-3.1018
0.0329
0.0275
5.2389
5.1614
14.7945
12.2154
2006
0
-2.8334
-3.0007
0.0317
0.0189
5.2879
5.1323
15.9836
13.2971
2007
0
-2.8345
-2.9096
0.0314
0.0151
5.3314
5.1024
16.0449
13.2619
2008
0
-2.8361
-2.8531
0.0310
0.0137
5.3753
5.0688
17.5710
14.4340
2009
0
-2.8361
-2.8478
0.0307
0.0125
5.4026
5.0187
17.7771
14.4573
2010
0
-2.8369
-2.8454
0.0303
0.0122
5.4279
4.9677
18.0307
14.4862
2011
0
-2.8382
-2.8477
0.0302
0.0119
5.4606
4.9230
18.3203
15.8297
2012
0
-2.8391
-2.8468
0.0300
0.0121
5.4968
4.8817
18.6180
15.8735
2013
0
-2.8401
-2.8483
0.0301
0.0110
5.5336
4.8394
18.9424
15.9427
2014
-50,000
-2.8415
-2.8473
0.0300
0.0109
5.5953
4.8770
18.1460
15.2665
2015
0
-2.8430
-2.8473
0.0300
0.0103
5.6561
4.9157
17.3567
14.6057
2016
0
-2.8439
-2.8473
0.0300
0.0105
5.7185
4.9563
16.5604
13.9452
2017
0
-2.8436
-2.8473
0.0300
0.0104
5.7826
4.9957
15.7101
13.2610
2018
0
-2.8423
-2.8473
0.0300
0.0100
5.8435
5.0321
14.8327
12.5886
2019
0
-2.8431
-2.8473
0.0300
0.0105
5.9027
5.0689
13.9549
11.9400
2020
0
-2.8438
-2.8473
0.0300
0.0108
5.9631
5.1053
13.0818
11.3106
2021
0
-2.8449
-2.8473
0.0300
0.0098
6.0423
5.1523
12.1935
10.6925
2022
0
-2.8460
-2.8473
0.0300
0.0117
6.1223
5.2007
11.2658
10.0499
2023
0
-2.8460
-2.8473
0.0300
0.0111
6.2016
5.2480
10.3280
9.4046
2024
-50,000
-2.8461
-2.8473
0.0300
0.0105
6.2155
5.2538
10.3248
9.4176
2025
0
-2.8463
-2.8473
0.0300
0.0099
6.2282
5.2581
10.3208
9.4420
2026
0
-2.8469
-2.8473
0.0300
0.0097
6.2436
5.2644
10.3084
9.4631
2027
0
-2.8476
-2.8473
0.0300
0.0117
6.2436
5.2648
10.2754
9.4658
2028
0
-2.8472
-2.8473
0.0300
0.0112
6.2453
5.2674
10.2361
9.4581
2029
0
-2.8469
-2.8473
0.0300
0.0106
6.2473
5.2701
10.1971
9.4462
2030
0
-2.8468
-2.8473
0.0300
0.0100
6.2472
5.2707
10.1689
9.4495
2031
0
-2.8468
-2.8473
0.0300
0.0099
6.2462
5.2695
10.1362
9.4432
2032
0
-2.8470
-2.8473
0.0300
0.0117
6.2441
5.2682
10.0944
9.4271
2033
0
-2.8468
-2.8473
0.0300
0.0114
6.2411
5.2652
10.0497
9.4033
2034
0
-2.8467
-2.8473
0.0300
0.0108
6.2385
5.2637
10.0070
9.3877
2035
0
-2.8466
-2.8473
0.0300
0.0101
6.2379
5.2631
9.9843
9.3740
2036
0
-2.8466
-2.8473
0.0300
0.0100
6.2393
5.2639
9.9690
9.3749
2037
0
-2.8467
-2.8473
0.0300
0.0115
6.2435
5.2678
9.9495
9.3648
2038
0
-2.8468
-2.8473
0.0300
0.0114
6.2461
5.2711
9.9275
9.3471
2039
0
-2.8470
-2.8473
0.0300
0.0110
6.2479
5.2732
9.9120
9.3334
2040
0
-2.8473
-2.8473
0.0300
0.0102
6.2483
5.2729
9.9027
9.3281
2041
0
-2.8476
-2.8473
0.0300
0.0099
6.2477
5.2707
9.8982
9.3270
2042
0
-2.8480
-2.8473
0.0300
0.0112
6.2478
5.2703
9.8964
9.3294
2043
0
-2.8484
-2.8473
0.0300
0.0113
6.2469
5.2700
9.8798
9.3134
2044
0
-2.8488
-2.8473
0.0300
0.0111
6.2457
5.2700
9.8694
9.3020
2045
0
-2.8492
-2.8473
0.0300
0.0103
6.2444
5.2702
9.8600
9.2999
2046
0
-2.8497
-2.8473
0.0300
0.0100
6.2436
5.2692
9.8610
9.2958
2047
0
-2.8503
-2.8473
0.0300
0.0111
6.2464
5.2706
9.8674
9.3086
2048
0
-2.8507
-2.8473
0.0300
0.0111
6.2483
5.2723
9.8601
9.2960
2049
0
-2.8510
-2.8473
0.0300
0.0109
6.2500
5.2738
9.8542
9.2902
2050
0
-2.8514
-2.8473
0.0300
0.0101
6.2501
5.2734
9.8488
9.2901
2051
0
-2.8517
-2.8473
0.0300
0.0099
6.2485
5.2717
9.8531
9.2927
2052
0
-2.8520
-2.8473
0.0300
0.0109
6.2496
5.2727
9.8573
9.3020
2053
0
-2.8522
-2.8473
0.0300
0.0110
6.2487
5.2713
9.8520
9.2962
2054
0
-2.8524
-2.8473
0.0300
0.0109
6.2475
5.2705
9.8446
9.2910
2055
0
-2.8525
-2.8473
0.0300
0.0103
6.2455
5.2688
9.8361
9.2859
2056
0
-2.8524
-2.8473
0.0300
0.0100
6.2418
5.2663
9.8389
9.2848
2057
0
-2.8524
-2.8473
0.0300
0.0109
6.2440
5.2679
9.8431
9.2950
2058
0
-2.8524
-2.8473
0.0300
0.0109
6.2455
5.2689
9.8399
9.2920
2059
0
-2.8524
-2.8473
0.0300
0.0107
6.2475
5.2705
9.8363
9.2940
2060
0
-2.8524
-2.8473
0.0300
0.0104
6.2488
5.2722
9.8381
9.2888
2061
0
-2.8525
-2.8473
0.0300
0.0102
6.2479
5.2724
9.8345
9.2894
2062
0
-2.8525
-2.8473
0.0300
0.0109
6.2479
5.2707
9.8385
9.2932
2063
0
-2.8525
-2.8473
0.0300
0.0108
6.2458
5.2684
9.8339
9.2893
2064
0
-2.8525
-2.8473
0.0300
0.0107
6.2438
5.2674
9.8291
9.2872
2065
0
-2.8525
-2.8473
0.0300
0.0106
6.2432
5.2676
9.8275
9.2850
2066
0
-2.8524
-2.8473
0.0300
0.0106
6.2461
5.2696
9.8265
9.2831
2067
0
-2.8524
-2.8473
0.0300
0.0108
6.2458
5.2695
9.8294
9.2862
2068
0
-2.8524
-2.8473
0.0300
0.0107
6.2460
5.2701
9.8294
9.2854
2069
0
-2.8525
-2.8473
0.0300
0.0107
6.2462
5.2705
9.8278
9.2856
2070
0
-2.8526
-2.8473
0.0300
0.0107
6.2465
5.2706
9.8248
9.2845
2071
0
-2.8528
-2.8473
0.0300
0.0107
6.2467
5.2704
9.8257
9.2818
2072
0
-2.8529
-2.8473
0.0300
0.0107
6.2468
5.2705
9.8253
9.2813
2073
0
-2.8530
-2.8473
0.0300
0.0107
6.2469
5.2707
9.8241
9.2838
2074
0
-2.8531
-2.8473
0.0300
0.0107
6.2470
5.2706
9.8218
9.2816
2075
0
-2.8532
-2.8473
0.0300
0.0107
6.2471
5.2707
9.8246
9.2820
2076
0
-2.8534
-2.8473
0.0300
0.0107
6.2471
5.2705
9.8233
9.2802
2077
0
-2.8535
-2.8473
0.0300
0.0107
6.2472
5.2705
9.8214
9.2803
2078
0
-2.8536
-2.8473
0.0300
0.0107
6.2472
5.2704
9.8190
9.2842
2079
0
-2.8537
-2.8473
0.0300
0.0107
6.2474
5.2705
9.8203
9.2839

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