# LifeTable¶

Commutation functions and actuarial notations

The LifeTable Space provides commutation functions and actuarial notations, such as $$D_{x}$$ and $$\require{enclose}{}_{f|}\overline{A}_{x}$$. Mortality tables are read from input.xlsx into an ExcelRange object. The ExcelRange object is bound to a Reference, MortalityTable.

This Space is included in:

Parameters

LifeTable Space is parameterized with Sex, IntRate and TableID:

>>> simplelife.LifeTable.parameters
('Sex', 'IntRate', 'TableID')


Each ItemSpace represents commutations functions actuarial notations for a combination of Sex, IntRate and TableID. For example, LifeTable['M', 0.03, 1] contains commutation functions and actuarial notations for Male, the interest rate of 3%, mortality table 1.

Sex

‘M’ or ‘F’ to indicate male or female column in the mortality table.

Type

str

IntRate

The constant interest rate for discounting.

Type

float

TableID

The identifier of the mortality table

Type

int

References

MortalityTable

ExcelRange object holding mortality tables. The data is read from MortalityTables range in input.xlsx.

Example

An example of LifeTable in the simplelife model:

>>> simplelife.LifeTable['M', 0.03, 1].AnnDuenx(40, 10)
8.725179890621531


Cells

 AnnDuenx(x, n[, k, f]) The present value of an annuity-due. AnnDuex(x, k[, f]) The present value of a lifetime annuity due. Ax(x[, f]) The present value of a lifetime assurance on a person at age x payable immediately upon death, optionally with an waiting period of f years. Axn(x, n[, f]) The present value of an assurance on a person at age x payable immediately upon death, optionally with an waiting period of f years. Cx(x) The commutation column $$\overline{C_x}$$. Dx(x) The commutation column $$D_{x} = l_{x}v^{x}$$. Exn(x, n) The value of an endowment on a person at age x payable after n years Mx(x) The commutation column $$M_x$$. Nx(x) The commutation column $$N_x$$. The discount factor $$v = 1/(1 + i)$$. dx(x) The number of persons who die between ages x and x+1 lx(x) The number of persons remaining at age x. qx(x) Probability that a person at age x will die in one year.
AnnDuenx(x, n, k=1, f=0)[source]

The present value of an annuity-due.

$\require{enclose}{}_{f|}\ddot{a}_{x:\enclose{actuarial}{n}}^{(k)}$
Parameters
• x (int) – age

• n (int) – length of annuity payments in years

• k (int, optional) – number of split payments in a year

• f (int, optional) – waiting period in years

AnnDuex(x, k, f=0)[source]

The present value of a lifetime annuity due.

Parameters
• x (int) – age

• k (int, optional) – number of split payments in a year

• f (int, optional) – waiting period in years

Ax(x, f=0)[source]

The present value of a lifetime assurance on a person at age x payable immediately upon death, optionally with an waiting period of f years.

$\require{enclose}{}_{f|}\overline{A}_{x}$
Axn(x, n, f=0)[source]

The present value of an assurance on a person at age x payable immediately upon death, optionally with an waiting period of f years.

$\require{enclose}{}_{f|}\overline{A}^{1}_{x:\enclose{actuarial}{n}}$
Cx(x)[source]

The commutation column $$\overline{C_x}$$.

Dx(x)[source]

The commutation column $$D_{x} = l_{x}v^{x}$$.

Exn(x, n)[source]

The value of an endowment on a person at age x payable after n years

${}_{n}E_x$
Mx(x)[source]

The commutation column $$M_x$$.

Nx(x)[source]

The commutation column $$N_x$$.

disc()[source]

The discount factor $$v = 1/(1 + i)$$.

dx(x)[source]

The number of persons who die between ages x and x+1

lx(x)[source]

The number of persons remaining at age x.

qx(x)[source]

Probability that a person at age x will die in one year.