Just Pensions

Part XI. Actuarial Tables for Calculation of Actuarial Values

The following two tables, known as actuarial commutation functions, can be used to calculate the actuarial present value of pension benefits. One table is for males and the other for females.

A value for the attained age will be used from the D(X) column as the denominator in the calculation.

A value, based on the retirement age, from one of the columns labeled N0(x), N2(x), N3.5(x), N4(x), will be used for the numerator in your calculation.

The column selected for the numerator will depend on the post-retirement cost-of-living provision of the pension. If no post-retirement cost-of-living select a value from the column headed N0(x), for post-retirement cost-of-living of 2.00% select a value from the column headed N2(x), etc.

For example, the actuarial present value of a pension without post-retirement cost-of-living of $1 per month for a male age 50 who will retire at age 60 has a numerator of 22703.473 (entry for age 60 from the column labeled N0(x) and a denominator of 395.817 (entry for age 50 from the column labeled D(X)).

Divide the numerator (22703.473) by the denominator (395.817) for a result of 57.36. The $57.36 represents the actuarial present value of a pension of $1.00 per month. to a male now age 50 starting at his age 60 and providing 2% per year cost-of-living increases after age 60.

If the monthly pension is $250, say, just multiply $250 by 57.36 getting $14,340.

The rule is: numerator value at retirement age over denominator at attained age times monthly pension amount equals the actuarial present value. The commutation functions are based on the UP-84 mortality table, setforward one year for males and setback five years for females, and an interest rate of 6.50%.

Table to Calculate Time Between Two Dates
Day Jan
[1]		 Feb
[2]		 Mar
[3]		 Apr
[4]		 May
[5]		 June
[6]		 Jul
[7]		 Aug
[8]		 Sep
[9]		 Oct
[10]		 Nov
[11]		 Dec
[12]		 Day
1 0.003 0.088 0.164 0.249 0.332 0.416 0.499 0.584 0.668 0.751 0.836 0.918 1
2 0.005 0.090 0.167 0.252 0.334 0.419 0.501 0.586 0.671 0.753 0.838 0.921 2
3 0.008 0.093 0.170 0.255 0.337 0.422 0.504 0.589 0.674 0.756 0.841 0.923 1
4 0.011 0.096 0.173 0.258 0.340 0.425 0.507 0.592 0.677 0.759 0.844 0.926 4
5 0.014 0.099 0.175 0.260 0.342 0.427 0.510 0.595 0.679 0.762 0.847 0.929 5
6 0.016 0.101 0.178 0.263 0.345 0.430 0.512 0.597 0.682 0.764 0.849 0.932 6
7 0.019 0.104 0.181 0.266 0.348 0.433 0.515 0.600 0.685 0.767 0.852 0.934 7
8 0.022 0.107 0.184 0.268 0.351 0.436 0.518 0.603 0.688 0.770 0.855 0.937 8
9 0.025 0.110 0.186 0.271 0.353 0.438 0.521 0.605 0.690 0.773 0.858 0.940 9
10 0.027 0.112 0.189 0.274 0.356 0.441 0.523 0.608 0.693 0.775 0.860 0.942 10
11 0.030 0.115 0.192 0.277 0.359 0.444 0.526 0.611 0.696 0.778 0.863 0.945 11
12 0.033 0.118 0.195 0.279 0.362 0.447 0.529 0.614 0.699 0.781 0.866 0.948 12
13 0.036 0.121 0.197 0.282 0.364 0.449 0.532 0.616 0.701 0.784 0.868 0.951 13
14 0.038 0.123 0.200 0.285 0.367 0.452 0.534 0.619 0.704 0.786 0.871 0.953 14
15 0.041 0.126 0.203 0.288 0.370 0.455 0.537 0.622 0.707 0.789 0.874 0.956 15
16 0.044 0.129 0.205 0.290 0.373 0.458 0.540 0.625 0.710 0.792 0.877 0.959 16
17 0.047 0.132 0.208 0.293 0.375 0.460 0.542 0.627 0.712 0.795 0.879 0.962 17
18 0.049 0.134 0.211 0.296 0.378 0.463 0.545 0.630 0.715 0.797 0.882 0.964 18
19 0.052 0.137 0.214 0.299 0.381 0.466 0.548 0.633 0.718 0.800 0.885 0.967 19
20 0.055 0.140 0.216 0.301 0.384 0.468 0.551 0.636 0.721 0.803 0.888 0.970 20
21 0.058 0.142 0.219 0.304 0.386 0.471 0.553 0.638 0.723 0.805 0.890 0.973 21
22 0.060 0.145 0.222 0.307 0.389 0.474 0.556 0.641 0.726 0.808 0.893 0.975 22
23 0.063 0.148 0.225 0.310 0.392 0.477 0.559 0.644 0.729 0.811 0.896 0.978 23
24 0.066 0.151 0.227 0.312 0.395 0.479 0.562 0.647 0.732 0.814 0.899 0.981 24
25 0.068 0.153 0.230 0.315 0.397 0.482 0.564 0.649 0.734 0.816 0.901 0.984 25
26 0.071 0.156 0.233 0.318 0.400 0.485 0.567 0.652 0.737 0.819 0.904 0.986 26
27 0.074 0.159 0.236 0.321 0.403 0.488 0.570 0.655 0.740 0.822 0.907 0.989 27
28 0.077 0.162 0.238 0.323 0.405 0.490 0.573 0.658 0.742 0.825 0.910 0.992 28
29 0.079 - 0.241 0.326 0.408 0.493 0.575 0.660 0.745 0.827 0.912 0.995 29
30 0.082 - 0.244 0.329 0.411 0.496 0.578 0.663 0.748 0.830 0.915 0.997 30
31 0.085 - 0.247 - 0.414 - 0.581 0.666 - 0.833 - 1.0 31
Day [1]
Jan		 [2]
Feb		 [3]
Mar		 [4]
Apr		 [5]
May		 [6]
June		 [7]
Jul		 [8]
Aug		 [9]
Sep		 [10]
Oct		 [11]
Nov		 [12]
Dec		 Day
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