Actuarial Tables Calculator
This calculator provides a simplified estimation of survival probabilities and expected future lifetime based on an illustrative mortality model. Actuarial tables, also known as mortality tables, are fundamental tools in actuarial science, used to predict the probability of death for individuals at different ages. These tables are crucial for pricing life insurance policies, calculating pension liabilities, and assessing various financial risks.
While real actuarial tables are complex and derived from vast demographic data, this calculator uses a simplified, illustrative formula to demonstrate the principles. It assumes a base mortality rate that increases exponentially with age, reflecting the general trend observed in human populations.
Understanding the Results
Probability of Surviving to Target Age: This is the likelihood, expressed as a percentage, that an individual currently at the "Current Age" will live to reach the "Target Age." It's calculated by multiplying the probabilities of surviving each year between the current and target ages.
Expected Additional Years of Life: Also known as "life expectancy at current age," this value represents the average number of additional years an individual of the "Current Age" is expected to live. It's calculated by summing the probabilities of surviving each subsequent year, up to a maximum age (e.g., 120 years in this calculator).
Important Disclaimer
This calculator uses a highly simplified and illustrative mortality model (q_x = 0.00001 * (1.1)^age, capped at 0.9999). It is NOT based on actual demographic data or real actuarial tables. The results are for educational and demonstrative purposes only and should not be used for financial planning, insurance decisions, or any real-world actuarial calculations. Real actuarial science involves much more sophisticated models, data analysis, and considerations.
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var calculateActuarial = function() {
var currentAgeInput = document.getElementById("currentAge");
var targetAgeInput = document.getElementById("targetAge");
var resultOutput = document.getElementById("resultOutput");
var currentAge = parseFloat(currentAgeInput.value);
var targetAge = parseFloat(targetAgeInput.value);
// Input validation
if (isNaN(currentAge) || isNaN(targetAge) || currentAge < 0 || targetAge = targetAge) {
resultOutput.innerHTML = "Target Age must be greater than Current Age for survival probability calculation.";
return;
}
if (currentAge > 119 || targetAge > 120) {
resultOutput.innerHTML = "Ages beyond 120 are outside the scope of this illustrative model.";
return;
}
// Simplified illustrative mortality rate function
// q_x = probability of dying within the next year at age x
// This is a simplified exponential model, not based on real data.
var getMortalityRate = function(age) {
if (age < 0) return 1.0; // Assume immediate death for negative ages
var q_x = 0.00001 * Math.pow(1.1, age);
return Math.min(q_x, 0.9999); // Cap mortality rate to prevent p_x from becoming 0 or negative
};
// 1. Calculate Probability of Surviving to Target Age
var survivalProbability = 1.0;
for (var age = currentAge; age < targetAge; age++) {
var q_age = getMortalityRate(age);
var p_age = 1 – q_age; // Probability of surviving one more year
survivalProbability *= p_age;
}
// 2. Calculate Expected Additional Years of Life (e_x)
var expectedYears = 0;
var cumulativeSurvivalProb = 1.0; // Probability of surviving from currentAge to currentAge + k
var maxAgeForCalculation = 120; // Sum up to a reasonable maximum age
for (var age = currentAge; age < maxAgeForCalculation; age++) {
var q_age = getMortalityRate(age);
var p_age = 1 – q_age;
cumulativeSurvivalProb *= p_age; // This is p_x * p_{x+1} * … * p_{age}
expectedYears += cumulativeSurvivalProb; // Summing _k p_x for k=1, 2, …
}
// Display results
resultOutput.innerHTML =
"Probability of Surviving to Age " + targetAge + ":
" + (survivalProbability * 100).toFixed(2) + "%" +
"Expected Additional Years of Life from Age " + currentAge + ":
" + expectedYears.toFixed(2) + " years";
};
// Run calculation on page load with default values
window.onload = function() {
calculateActuarial();
};