Life Table & Annuity Values

Mortality table analytics — l_x, q_x, life expectancy, and commutation functions for annuity/insurance pricing.

Mortality table (q_x)

q_x values, comma/space separated, indexed from age 0

0.006203, 0.000803, 0.000503, 0.000404, 0.000354, 0.000204, 0.000205, 0.000205, 0.000206, 0.000206, 0.000207, 0.000208, 0.000208, 0.000209, 0.000210, 0.000211, 0.000212, 0.000214, 0.000215, 0.000217, 0.000218, 0.000220, 0.000222, 0.000224, 0.000227, 0.000229, 0.000232, 0.000235, 0.000239, 0.000243, 0.000247, 0.000252, 0.000257, 0.000263, 0.000269, 0.000276, 0.000283, 0.000292, 0.000301, 0.000311, 0.000322, 0.000334, 0.000348, 0.000363, 0.000379, 0.000397, 0.000416, 0.000438, 0.000462, 0.000488, 0.000517, 0.000549, 0.000584, 0.000622, 0.000664, 0.000710, 0.000762, 0.000818, 0.000879, 0.000947, 0.001022, 0.001104, 0.001195, 0.001294, 0.001404, 0.001524, 0.001656, 0.001802, 0.001962, 0.002138, 0.002332, 0.002546, 0.002780, 0.003038, 0.003322, 0.003634, 0.003978, 0.004355, 0.004771, 0.005228, 0.005731, 0.006284, 0.006892, 0.007561, 0.008297, 0.009107, 0.009998, 0.010978, 0.012056, 0.013241, 0.014545, 0.015980, 0.017558, 0.019293, 0.021203, 0.023303, 0.025613, 0.028155, 0.030950, 0.034025, 0.037408, 0.041128, 0.045221, 0.049723, 0.054676, 0.060123, 0.066116, 0.072707, 0.079958, 0.087934, 0.096707

Age (x)

Interest rate (i)

Term (n years)

Table window (± years)

Life table (age 35–55)

Age x	q_x	p_x	l_x	d_x	e_x
35	0.028%	99.972%	98,511.0	27.2	66.42
36	0.028%	99.972%	98,483.8	27.9	65.44
37	0.029%	99.971%	98,456.0	28.7	64.46
38	0.030%	99.970%	98,427.2	29.6	63.48
39	0.031%	99.969%	98,397.6	30.6	62.50
40	0.032%	99.968%	98,367.0	31.7	61.52
41	0.033%	99.967%	98,335.3	32.8	60.54
42	0.035%	99.965%	98,302.5	34.2	59.56
43	0.036%	99.964%	98,268.3	35.7	58.58
44	0.038%	99.962%	98,232.6	37.2	57.60
45	0.040%	99.960%	98,195.4	39.0	56.62
46	0.042%	99.958%	98,156.4	40.8	55.64
47	0.044%	99.956%	98,115.5	43.0	54.67
48	0.046%	99.954%	98,072.6	45.3	53.69
49	0.049%	99.951%	98,027.3	47.8	52.72
50	0.052%	99.948%	97,979.4	50.7	51.74
51	0.055%	99.945%	97,928.8	53.8	50.77
52	0.058%	99.942%	97,875.0	57.2	49.80
53	0.062%	99.938%	97,817.8	60.8	48.83
54	0.066%	99.934%	97,757.0	64.9	47.86
55	0.071%	99.929%	97,692.1	69.4	46.89

Insurance & annuity values at age 45, i = 4.00%

Function	Whole life	20-year term
Insurance (A_x)	0.0955	0.0094
Annuity-due (ä_x)	22.867	14.068
Annuity-immediate (a_x)	21.892	13.518
Pure endowment (20E_x)	—	0.4495

Survivorship curve (l_x)

Assumptions & limitations

Discrete (annual) age-at-death and level effective annual interest rate i are assumed; no select/ultimate distinction.
Insurance/annuity present values use a backward recursion over the pasted (or illustrative Makeham-form) q_x table starting at age 0.
The illustrative sample mortality curve is for demonstration only and should not be used for pricing; substitute a published/experience table.