Life table and life expectancy

Q_x, survival probabilities, curtate and complete life expectancy from the Makeham law of the SOA Standard Ultimate Life Table or your own mortality rates.

Inputs

MortalityAge xSurvive foryears

Results

q_65: death within a year

0.5915%

10p65: survive 10 years

90.086%

Curtate life expectancy e_x

22.24 years

Complete life expectancy

22.74 years

Expected age at death 87.7

Survivors from age x, out of 100,000

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Life table

Age	q_x	l_x	d_x	e_x
65	0.005915	100,000	591	22.24
66	0.006619	99,409	658	21.37
67	0.007409	98,751	732	20.52
68	0.008297	98,019	813	19.67
69	0.009294	97,206	903	18.83
70	0.010413	96,302	1,003	18.01
71	0.011670	95,299	1,112	17.20
72	0.013081	94,187	1,232	16.40
73	0.014664	92,955	1,363	15.62
74	0.016440	91,592	1,506	14.85
75	0.018433	90,086	1,661	14.10
76	0.020668	88,426	1,828	13.37
77	0.023175	86,598	2,007	12.65
78	0.025984	84,591	2,198	11.95
79	0.029132	82,393	2,400	11.27
80	0.032658	79,993	2,612	10.61
81	0.036607	77,381	2,833	9.96
82	0.041025	74,548	3,058	9.34
83	0.045968	71,490	3,286	8.74
84	0.051493	68,203	3,512	8.16
85	0.057665	64,691	3,730	7.61
86	0.064554	60,961	3,935	7.07
87	0.072237	57,026	4,119	6.56
88	0.080798	52,906	4,275	6.07
89	0.090326	48,632	4,393	5.60
90	0.100917	44,239	4,464	5.16
91	0.112675	39,774	4,482	4.74
92	0.125708	35,293	4,437	4.34
93	0.140128	30,856	4,324	3.97
94	0.156052	26,532	4,140	3.61
95	0.173599	22,392	3,887	3.28
96	0.192887	18,505	3,569	2.97
97	0.214030	14,935	3,197	2.68
98	0.237134	11,739	2,784	2.41
99	0.262294	8,955	2,349	2.16
100	0.289584	6,606	1,913	1.93
101	0.319055	4,693	1,497	1.71
102	0.350723	3,196	1,121	1.52
103	0.384564	2,075	798	1.34
104	0.420500	1,277	537	1.17
105	0.458393	740	339	1.02
106	0.498036	401	200	0.88
107	0.539141	201	108	0.76
108	0.581339	93	54	0.65
109	0.624175	39	24	0.55
110	0.667114	15	10	0.46
111	0.709550	5	3	0.38
112	0.750825	1	1	0.31
113	0.790259	0	0	0.25
114	0.827184	0	0	0.20
115	0.860987	0	0	0.16
116	0.891156	0	0	0.12
117	0.917323	0	0	0.09
118	0.939306	0	0	0.06

Methodology

Conventions

Mortality follows Makeham's law μ_x = A + B c^x (the SOA Standard Ultimate Life Table uses A = 0.00022, B = 2.7×10⁻⁶, c = 1.124), or your own table of q_x.
Within a year of age, a table assumes a uniform distribution of deaths. The table ends at age 120.

References

Dickson, Hardy and Waters, Actuarial Mathematics for Life Contingent Risks, 3rd ed.
Society of Actuaries, Standard Ultimate Life Table (LTAM exam tables).

Formulas

Survival under Makeham: {}_tp_x = \exp\!\Big(-A t - \frac{B c^x (c^t - 1)}{\ln c}\Big)
Mortality rate: q_x = 1 - p_x,\quad d_x = l_x q_x
Curtate expectation: e_x = \sum_{k \ge 1} {}_kp_x
Complete expectation: \mathring{e}_x = \int_0^\infty {}_tp_x\,dt \approx e_x + \tfrac12