SSA Releases “Life Tables for the US Social Security Area 1900-2100”

Actuarial Study No. 120 displays life tables based on historical and projected mortality in the area
covered by the United States Social Security program. This projected mortality was used in estimating the future costs for the Old-Age, Survivors, and Disability Insurance (OASDI) program included in the 2005 Report of the OASDI Board of Trustees to Congress. A web address for this and other Actuarial Studies is www.socialsecurity.gov/OACT/NOTES/actstud.html.

Warning:  this study is not for the math-impaired.  Here’s a sample of the text:

    The life table functions lx, dx, Lx, Tx, and were calculated
as follows:

l0 = 100,000
dx = lx • 1qx x = 1, 2, 3, …
lx = lx-1 • (1 – 1qx-1) x = 1, 2, 3, …
L0 = l0 – 1f0 • d0
Lx = lx – .5 • dx x = 1, 2, 3, …
Tx = Lx + Lx+1 + Lx+2 + … + L148 x = 0, 1, 2, 3, …
= Tx / lx x = 0, 1, 2, 3, …

***

One method that has been used to calculate probabilities of
death for a life table that are consistent with the underlying
pattern of mortality experienced in the population is to
require that the life table central death rates for quinquennial
age groups, 5mx, equal the population central death rates,
5Mx. That is 5mx = 5Mx for x = 5, 10, 15, …, 90
Unfortunately, making these central death rates equal may
introduce error when they should differ because the age distribution
within the quinquennial age groups in the stationary
population implied by the life table differs from that in the
actual population under study. The degree of consistency can
be improved using the relationship,

5mx =
dx + dx+1 + dx+2 + dx+3 + dx+4
Lx + Lx+1 + Lx+2 + Lx+3 + Lx+4
=
dx •Lx+
dx+1 •Lx+1+
dx+2 •Lx+2+
dx+3 •Lx+3+
dx+4 •Lx+4 Lx Lx+1 Lx+2 Lx+3 Lx+4
Lx + Lx+1 + Lx+2 + Lx+3 + Lx+4
=
mx•Lx + mx+1•Lx+1 + mx+2•Lx+2 + mx+3•Lx+3 + mx+4•Lx+4
Lx + Lx+1 + Lx+2 + Lx+3 + Lx+4

If you understand that, then this publication is for you!