Mortality Stopnja Kalkulator

A crude mortality rate is the total number of deaths in a population divided by the total population size, expressed per 1,000 or 100,000 people per year. It is simple to calculate but does not account for differences in population age structure — a country with an older population will have a higher crude mortality rate even if age-specific death rates are identical to a younger country. An age-specific mortality rate calculates the death rate for a defined age group (e.g., deaths per 1,000 people aged 65–74). A standardized (or age-adjusted) mortality rate uses a reference standard population to remove the confounding effect of age distribution differences, enabling fair comparison of mortality rates across populations or time periods with different age structures. Actuaries typically work with age-specific rates derived from life tables, which provide the most detailed and applicable information for pricing and reserving.

Several standard mortality tables are used for different insurance and pension applications in the United States. The 2017 Commissioners Standard Ordinary (CSO) table is mandated by state insurance regulations for life insurance premium valuation and reserve calculation. The 2012 Individual Annuity Mortality (IAM) table (with projection scale MP) is used for individual annuity pricing and reserving. The RP-2014 (Retirement Plans) table with MP-2021 improvement scale is the current standard for pension plan mortality assumptions under ERISA and IRS regulations. The Social Security Administration publishes period life tables annually for Social Security program actuarial analysis. The CDC National Center for Health Statistics publishes national life tables based on vital statistics. Actuaries select the appropriate table based on the product type, the characteristics of the insured population, and regulatory requirements.

Select mortality tables recognize that individuals who have recently undergone insurance underwriting are, on average, healthier than the general population at the same age. The select period covers the years immediately after policy issue (typically 5–15 years) during which recent underwriting provides a favorable mortality advantage. After the select period, the insured population's mortality is assumed to converge toward the general population level, called 'ultimate' mortality. A select-and-ultimate table thus shows lower mortality rates in the select years following policy issue, gradually increasing to the ultimate level. This distinction is important for accurately pricing policies and calculating reserves: applying ultimate mortality to recently underwritten lives would overstate mortality costs and overprice new insurance products.

Women have consistently lower mortality rates than men at virtually every age in developed countries, primarily due to biological factors and behavioral differences in risk-taking, healthcare utilization, and lifestyle choices. At age 40, female mortality rates are approximately 40–50% lower than male rates. This difference narrows with advancing age but persists throughout the lifespan. Historically, insurance companies priced life insurance and annuities using gender-distinct mortality tables — women paid lower life insurance premiums (lower mortality risk) but received smaller annuity payments (longer expected payout period). In the European Union, the 2011 Test-Achats ruling by the European Court of Justice prohibited the use of gender in insurance pricing, requiring unisex tables. The United States continues to permit gender-distinct pricing for most insurance products, though some states restrict its use in specific contexts.

Mortality improvement refers to the long-term trend of declining age-specific death rates over time, driven by advances in medicine, public health, nutrition, and lifestyle changes. For insurance and pension purposes, mortality improvement matters because products and obligations that extend over decades must account for the expectation that future mortality rates will be lower than current rates — meaning annuitants will live longer and pension beneficiaries will draw benefits for more years. Actuaries apply mortality improvement scales (such as the SOA's MP-2021 scale) that project age-specific annual percentage reductions in mortality rates into the future. Failing to account for mortality improvement systematically understates annuity liabilities and pension obligations, leading to underfunding and actuarial losses. The projection of mortality improvement is one of the most uncertain — and consequential — assumptions in long-term actuarial work.

The Gompertz model, developed by Benjamin Gompertz in 1825, is a mathematical formula that describes the exponential increase in human mortality rates with age: mu_x = Ae^(Bx), where mu_x is the force of mortality at age x and A and B are constants estimated from life table data. The model captures the observed phenomenon of roughly doubling mortality risk with each 8–9 additional years of age in the adult population. Makeham extended the model by adding a constant term C representing age-independent background mortality from accidents and other non-age-related causes: mu_x = A + Be^(Cx). These parametric models are used when full life table data is not available, for smoothing raw mortality data, for mortality projection purposes, and in certain closed-form actuarial calculations. They represent foundational tools in actuarial mathematics and demographic mortality modeling.

Life expectancy is the expected (average) number of years a person of a given age will live, calculated from current or projected mortality rates. It is a statistical average — roughly half the population will die before reaching life expectancy and half will live longer. Maximum lifespan refers to the biological upper limit of human longevity — the oldest reliably documented human age was 122 years (Jeanne Calment, France, 1875–1997). For actuarial purposes, mortality tables typically extend to age 120 or even 125 with very small but non-zero mortality rates. From a financial planning perspective, life expectancy provides a midpoint estimate while maximum lifespan defines the tail risk that financial plans must consider — the scenario where an individual lives to 95 or 100 and must fund many decades of retirement. Planning only to life expectancy leaves a 50% probability of outliving your financial resources.