Ordinary Annuity (End of Period)
Annuity Due (Beginning of Period)
Calculation Results
Future Value:
Total Contributions:
Total Interest Earned:
What is the Future Value of an Annuity?
The Future Value (FV) of an annuity is a financial metric used to calculate the total value of a series of recurring payments at a specific date in the future, assuming a fixed interest rate. This tool is essential for retirement planning, savings goals, and understanding the long-term impact of compound interest on regular investments.
Ordinary Annuity vs. Annuity Due
The timing of your payments significantly impacts the final sum:
Ordinary Annuity: Payments are made at the end of each period (e.g., a monthly savings deposit made on the last day of the month).
Annuity Due: Payments are made at the beginning of each period (e.g., rent or a savings deposit made on the first day of the month). Annuity dues generally result in a higher future value because each payment has one extra period to earn interest.
The Mathematical Formula
The formula for an Ordinary Annuity is:
FV = P × [((1 + r)^n – 1) / r]
Where:
FV = Future Value
P = Periodic Payment
r = Interest rate per period (Annual Rate / Frequency)
n = Total number of periods (Years × Frequency)
Realistic Example
Imagine you invest $200 every month into an index fund for 20 years with an expected annual return of 8%.
Payment (P): $200
Annual Rate: 8% (0.08)
Frequency: 12 (Monthly)
Periods (n): 20 × 12 = 240 months
Rate per period (r): 0.08 / 12 = 0.006667
Using the Ordinary Annuity formula, your investment would grow to approximately $117,804.08 after 20 years, even though you only contributed $48,000 out of pocket.
function calculateFV() {
var P = parseFloat(document.getElementById('periodicPayment').value);
var annualRate = parseFloat(document.getElementById('annualRate').value);
var years = parseFloat(document.getElementById('years').value);
var frequency = parseInt(document.getElementById('frequency').value);
var type = document.getElementById('annuityType').value;
if (isNaN(P) || isNaN(annualRate) || isNaN(years) || P <= 0 || years <= 0) {
alert("Please enter valid positive numbers for all fields.");
return;
}
// Convert annual rate to periodic decimal rate
var r = (annualRate / 100) / frequency;
// Total number of periods
var n = years * frequency;
var fv = 0;
if (r === 0) {
// If interest rate is 0, it's just a sum of payments
fv = P * n;
} else {
// Formula: FV = P * [((1 + r)^n – 1) / r]
fv = P * (Math.pow(1 + r, n) – 1) / r;
// Adjust for Annuity Due (payment at beginning of period)
if (type === "due") {
fv = fv * (1 + r);
}
}
var totalInvested = P * n;
var totalInterest = fv – totalInvested;
// Formatting results
document.getElementById('fvResult').innerText = "$" + fv.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('totalContrib').innerText = "$" + totalInvested.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('totalInterest').innerText = "$" + totalInterest.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('resultArea').style.display = "block";
}