Life insurance calculations

Life insurers use mathematicians called actuaries to calculate what premiums should be charged for life insurance. The actuaries based their calculations on mortality tables, as per the example on this pdf.

If you refer to the first and second rows of the table you will see that, out of 100,000 male babies born, 598 die before they are one year old and 99,402 are still living at age one. Out of 100,000 female babies born, 484 die before they are one year old and 99,516 are still living at age one.

In the second and third rows of the table which corresponds to the second and third years of age, 44 male babies will have died aged one last birthday and 99,358 survive to the age of two. For females, 31 male babies will have died aged one last birthday and 99,486 survive to the age of two.

Each row shows the numbers of males and females dying and surviving at each subsequent year of age until, at age 111, not a single survivor out of the original 100,000 remains alive.

What the columns mean

The qx column in the table is the probability that a person aged x will die before reaching x+ 1, and is thus the mortality rate for that age.

The ex column is the expectation of life for a person aged x. Thus a male aged 40 can expect to live on average a further 37.657 years.