Mortality Tables and Actuarial Pricing

Life insurers and annuity providers need a number that no single person can give them: the probability that a person of a given age, sex, and health status dies within the next year. No individual life tells you this — but a mortality table, built from the observed deaths of millions of people across many years, gives a stable, reliable estimate of that probability for each age, and that table is the foundation underneath essentially every life insurance premium and annuity payout in the industry.

What a mortality table actually contains

A mortality table lists, for each age, the probability of death within the next year — commonly written $q_x$, the probability someone aged $x$ dies before reaching age $x+1$. These probabilities are built from large population studies (insured lives, in the US often the Society of Actuaries' tables), separated by sex and sometimes by smoking status or underwriting class, because these factors meaningfully shift the death probability at a given age. From the table, actuaries derive everything else they need: life expectancy at any age, the probability of surviving to a given future age, and ultimately the expected cost of a death benefit or the expected number of payments an annuity will make.

Pricing then works by taking the expected cost, spread across all the ages a policy might pay out, and discounting it back to today using an assumed interest rate, then adding a margin for expenses and profit. For example, a life insurer pricing a policy for a 40-year-old non-smoker uses the mortality table's $q_{40}, q_{41}, \ldots$ sequence to calculate the probability-weighted expected value of the death benefit across all the years the policy could pay out, and sets the premium so that, averaged across a large pool of similar policyholders, premiums collected cover expected claims plus a margin — even though any individual policyholder's actual date of death is completely unknown.

What this means in practice

The table only works because it's applied to a large pool — insurers are relying on the law of large numbers to make an unpredictable individual outcome (one person's death) into a predictable aggregate one (a large pool's death rate), which is the entire mechanism that makes life insurance and annuity pricing possible in the first place. Insurers periodically update mortality tables as life expectancy shifts (generally improving over time), and using a stale table is a real pricing risk — annuities in particular become underpriced if people live systematically longer than an old table assumed.