Mortality Tables Explained: How Life Insurance Math Works

A mortality table is a chart showing how likely people are to die at each age. For every age, it lists the number alive out of a starting group — usually 100,000 newborns. Insurers build these tables from millions of real death records.

This matters because life insurance is a business of promises about the future. To promise a family a payment when someone dies, an insurer must know how many policyholders will die this year on average. The mortality table turns that guesswork into solid numbers.

Key Concepts

• l_x — the number of people alive at exact age x, out of the original group l_0 (usually 100,000).
• d_x — the number of people who die between age x and age x+1, so d_x = l_x − l_{x+1}.
• q_x — the probability that a person aged exactly x dies before reaching age x+1. It is calculated as q_x = d_x / l_x.
• p_x — the probability that a person aged x survives to age x+1, so p_x = 1 − q_x.
• Select vs ultimate tables — select tables use data from newly insured lives (healthier at first); ultimate tables cover everyone.
• Omega (ω) — the limiting age of the table, the highest age listed, often 110 or 120, where l_ω = 0.

Formulas

• q_x = d_x / l_x — probability of death within the year of age x. Applies to a cohort of identical lives; assumes deaths spread across the year.
• _n p_x = l_{x+n} / l_x — probability that a person aged x survives n years.
• _n q_x = (l_x − l_{x+n}) / l_x — probability that a person aged x dies within the next n years.
• Life expectancy e_x ≈ (l_x + l_{x+1} + l_{x+2} + … + l_ω) / l_x — the average future years lived by a person aged x; uses whole-year approximations.

Worked Example

Suppose a mortality table shows: l_40 = 97,000 and l_41 = 96,760. This means out of 100,000 newborns, 97,000 reach age 40.

1. Step 1: Find deaths in the year of age 40: d_40 = l_40 − l_41 = 97,000 − 96,760 = 240.
2. Step 2: Probability a 40-year-old dies before 41: q_40 = d_40 / l_40 = 240 / 97,000 ≈ 0.00247, about 0.25%.
3. Step 3: Probability of surviving the year: p_40 = 1 − q_40 = 1 − 0.00247 = 0.99753, about 99.75%.
4. Step 4: If the insurer sells 10,000 policies to 40-year-olds, expected deaths this year = 10,000 × 0.00247 ≈ 24.7, roughly 25 claims.

Common Misconceptions

• "The table predicts when I will die." It does not. It gives group averages. Your personal outcome is unknown; only the average over thousands of people is reliable.
• "Mortality tables stay the same forever." They change. As medicine and living conditions improve, people live longer, so insurers regularly update tables with fresh data.
• "q_x is the same as d_x." Not the same: d_x is a count of deaths (240 people); q_x is a probability (0.00247). They answer different questions.

Real-World Applications

• Life insurance pricing — insurers use q_x to estimate claims and set premiums so the company stays solvent.
• Pensions and retirement funds — pension providers use mortality tables to estimate how long retirees will live and how much money must be set aside.
• Public health — governments compare life expectancy across regions and years to measure health progress.

Mortality tables are the foundation of all life insurance mathematics. From the simple ratio q_x = d_x / l_x, actuaries build survival probabilities, life expectancies and the claim counts that make insurance pricing possible.