Life Insurance & Mortality Table

A mortality table is essentially a record, based on past experience, that shows the number of persons living at successive ages out of an original group of given size. For convenience, the original group is usually taken as 100 000 or 1 000 000 at age one. The table also includes information other than the number of persons living at successive ages.

One of the widely used mortality used at the present time is the Commissioner 1941 Standard Ordinary Mortality table (usually referred to as the CSO table).

If we denote by Ix the number of persons from the original group who live to attain the age x, then the table shows that I5 = 983 817, I50 = 810 900 etc. Clearly the numbers that die in any year can be obtained as the difference living at consecutive ages. Thus

I₁₀-I₁₁=971804-969890=1914

persons died between the ages of ten and eleven. If we denote by d_x the number of persons in the original group that attain age x but die before reaching age x+1, then clearly

d_x=I_x-I_x+1

Thus d₅₀ = 9 900 means that 9 900 persons out of the original 1 000 000 died during their fiftieth year of life. Since I_x persons attain age x and I_x+1 of these also reach age x+1, the probability

P_x= I_x+1 / I_x

is called the probability of survival for persons of age x. Likewise, since d_x persons die between the ages x and x+1, the probability

Q_x= d_z/I_x

is called the rate of mortality, or death probability, for persons of age x. The mortality tables is the foundation of life insurance and life annuities and is therefore of fundamental importance. It should be clear that a mortality table based on a given group will not agree exactly with another table based on a different group. For example, wide differences are found in the rate of mortality according to race, sex, occupation, standard of living and various other factors. Consequently, there are numerous mortality tables in actual use, and many of these revised from time to time as medical science progress and general health conditions improve, thus increasing the span of life. Most life insurance companies use at least two mortality tables: one for life insurance and a different one for life annuities. For if people die more rapidly than predicted by the mortality table, the company pays out faster on insurance policies and life annuities.

The fundamental principle that makes life insurance and life annuities sound is that persons of a given class do tend to die with approximately the same regularity as indicated by a mortality table made up of such group.

Example: The graduating class of a university contained 500 students aged twenty-one. According to the CSO table, how many of these will be alive to celebrate their fiftieth reunion of their class?

Solution: The question is, essentially, how many of these 500 students will live to attain the age of seventy-one. The CSO table gives I₂₁ =949 171 and I₇₁ =427 593. Consequently the expected number is

500x(I₇₁/I₂₁)=500x(427593/949171)=225