.actuarial-calculator-container {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
max-width: 800px;
margin: 0 auto;
padding: 20px;
background: #f9fbfd;
border: 1px solid #e1e4e8;
border-radius: 8px;
}
.actuarial-calculator-container h2 {
text-align: center;
color: #2c3e50;
margin-bottom: 25px;
}
.calc-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
@media (max-width: 600px) {
.calc-grid {
grid-template-columns: 1fr;
}
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
color: #34495e;
font-size: 0.95em;
}
.input-group input {
width: 100%;
padding: 10px;
border: 1px solid #cbd5e0;
border-radius: 4px;
font-size: 1em;
box-sizing: border-box;
}
.input-group input:focus {
border-color: #3498db;
outline: none;
box-shadow: 0 0 0 3px rgba(52, 152, 219, 0.1);
}
.calc-btn {
grid-column: 1 / -1;
background-color: #2c3e50;
color: white;
padding: 12px;
border: none;
border-radius: 4px;
font-size: 1.1em;
cursor: pointer;
transition: background 0.3s;
margin-top: 10px;
font-weight: bold;
}
.calc-btn:hover {
background-color: #1a252f;
}
.result-section {
grid-column: 1 / -1;
margin-top: 25px;
background: #fff;
padding: 20px;
border-radius: 6px;
box-shadow: 0 2px 4px rgba(0,0,0,0.05);
border-left: 5px solid #2c3e50;
display: none;
}
.result-row {
display: flex;
justify-content: space-between;
padding: 10px 0;
border-bottom: 1px solid #eee;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
color: #7f8c8d;
font-weight: 500;
}
.result-value {
font-weight: 700;
color: #2c3e50;
}
.final-result {
font-size: 1.4em;
color: #27ae60;
}
.error-msg {
color: #e74c3c;
text-align: center;
margin-top: 10px;
font-weight: bold;
display: none;
}
.info-icon {
font-size: 0.8em;
color: #95a5a6;
cursor: help;
}
function calculateActuarialValue() {
var benefit = document.getElementById('futureBenefit').value;
var years = document.getElementById('timeHorizon').value;
var rate = document.getElementById('discountRate').value;
var prob = document.getElementById('probability').value;
var resultBox = document.getElementById('resultSection');
var errorBox = document.getElementById('errorMsg');
// Reset display
resultBox.style.display = "none";
errorBox.style.display = "none";
// Validation
if (benefit === "" || years === "" || rate === "" || prob === "") {
errorBox.innerText = "Please fill in all fields.";
errorBox.style.display = "block";
return;
}
var benefitVal = parseFloat(benefit);
var yearsVal = parseFloat(years);
var rateVal = parseFloat(rate);
var probVal = parseFloat(prob);
if (isNaN(benefitVal) || isNaN(yearsVal) || isNaN(rateVal) || isNaN(probVal)) {
errorBox.innerText = "Please enter valid numbers.";
errorBox.style.display = "block";
return;
}
if (probVal 100) {
errorBox.innerText = "Probability must be between 0 and 100.";
errorBox.style.display = "block";
return;
}
// Calculation Logic
// 1. Calculate Discount Factor: 1 / (1 + r)^n
var decimalRate = rateVal / 100;
var discountFactor = 1 / Math.pow((1 + decimalRate), yearsVal);
// 2. Calculate Unadjusted Present Value (Time Value of Money only)
var unadjustedPV = benefitVal * discountFactor;
// 3. Apply Probability (Actuarial Adjustment)
var decimalProb = probVal / 100;
var actuarialPV = unadjustedPV * decimalProb;
// Update UI
document.getElementById('resDiscountFactor').innerText = discountFactor.toFixed(4);
document.getElementById('resProbability').innerText = decimalProb.toFixed(2);
document.getElementById('resUnadjusted').innerText = "$" + unadjustedPV.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('resAPV').innerText = "$" + actuarialPV.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
resultBox.style.display = "block";
}
Actuarial Present Value Calculator
Please enter valid numeric values for all fields.
Discount Factor:
Probability Factor:
Unadjusted Present Value:
Actuarial Present Value (APV):
Actuarial Rate Calculator: Understanding Present Value and Risk
The Actuarial Rate Calculator is a specialized tool designed to determine the Actuarial Present Value (APV) of a future financial obligation or benefit. Unlike standard financial calculators that only account for the time value of money (interest), an actuarial calculation incorporates probability and contingency.
This tool is essential for evaluating pensions, insurance settlements, court judgments with contingent payouts, or any financial scenario where a future payment is not guaranteed but depends on a specific event (such as survival, occurrence of a hazard, or legal ruling).
How to Use This Calculator
To obtain an accurate actuarial valuation, input the following metrics:
- Contingent Benefit Amount: The specific lump sum or value expected to be paid in the future.
- Time Horizon: The number of years until the payment is expected to be made.
- Actuarial Discount Rate: The assumed annual rate of return or technical interest rate used to discount the future value back to today's dollars. In pension valuation, this is often set by regulation or market bond yields.
- Probability of Occurrence: The statistical likelihood (0-100%) that the condition for payment will be met (e.g., probability of survival to age 65).
Understanding the Formula
The calculator uses standard actuarial mathematics combining the Time Value of Money with Probability Theory.
APV = Benefit × (1 + i)-n × p
Where:
- APV: Actuarial Present Value
- i: Annual Discount Rate (decimal)
- n: Number of years
- p: Probability of the event occurring (0.0 to 1.0)
Application in Real Scenarios
1. Pension Commutation: When an employee chooses to take a lump sum instead of a lifetime monthly pension, actuaries must calculate the present value of those potential future payments, adjusted for the likelihood of the employee living to receive them.
2. Legal Settlements: In structured settlements or damages for future lost wages, the amount is discounted not just by interest, but by the probability that the plaintiff would have continued working if the incident had not occurred.
Key Definitions
- Discount Rate
- Also known as the "technical rate" or "hurdle rate," this percentage reflects the expected return on capital. A higher discount rate results in a lower present value.
- Contingency
- A condition that must be met for a payout to occur. In life insurance, death is the contingency; in annuities, survival is the contingency.