An annuity is a financial product that pays out a fixed stream of payments to an individual over time. These payments can be made on a regular schedule, such as monthly, quarterly, or annually. Annuities are often used for retirement planning, providing a steady income stream after an individual stops working.
The calculation of an annuity's future value is crucial for understanding how an investment will grow over time, assuming regular contributions and a consistent interest rate. This calculator helps you determine the total accumulated amount, including all your contributions and the generated interest, at the end of a specified period.
The Formula for Future Value of an Ordinary Annuity
An ordinary annuity is one where the payments are made at the end of each period. The formula to calculate the Future Value (FV) of an ordinary annuity is:
FV = P * [((1 + r)^n - 1) / r]
FV = Future Value of the annuity
P = The amount of each periodic payment
r = The periodic interest rate (as a decimal)
n = The total number of periods
How the Calculator Works
This calculator takes three inputs:
Periodic Payment Amount (P): The fixed amount you contribute or receive at the end of each period.
Periodic Interest Rate (r): The interest rate applied to the annuity balance for each period. It must be entered as a decimal (e.g., 5% should be entered as 0.05).
Number of Periods (n): The total number of payment periods over which the annuity will exist or grow.
Using the formula above, the calculator computes the total future value, showing you the accumulated wealth after all payments and interest accruals.
Example Calculation
Let's say you plan to invest $100 (Periodic Payment, P) at the end of each month for 10 years (Number of Periods, n). If the monthly interest rate is 0.5% (Periodic Interest Rate, r = 0.005), the future value would be calculated as follows:
FV = 100 * [((1 + 0.005)^120 - 1) / 0.005]
FV = 100 * [((1.005)^120 - 1) / 0.005]
FV = 100 * [(1.8193967 - 1) / 0.005]
FV = 100 * [0.8193967 / 0.005]
FV = 100 * 1638.7934
FV ≈ $163,879.34
So, after 10 years, your investment would have grown to approximately $163,879.34.
Use Cases
Retirement Planning: Estimating the future value of your retirement savings.
Investment Growth: Projecting how regular investments will accumulate over time.
Savings Goals: Determining the potential growth of a savings fund with regular contributions.
Financial Education: Demonstrating the power of compounding interest.
function calculateAnnuity() {
var periodicPayment = parseFloat(document.getElementById("periodicPayment").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var numberOfPeriods = parseFloat(document.getElementById("numberOfPeriods").value);
var errorMessageDiv = document.getElementById("errorMessage");
var annuityValueDiv = document.getElementById("annuityValue");
errorMessageDiv.textContent = ""; // Clear previous errors
annuityValueDiv.textContent = "–"; // Reset result
// Input validation
if (isNaN(periodicPayment) || periodicPayment <= 0) {
errorMessageDiv.textContent = "Please enter a valid positive number for Periodic Payment Amount.";
return;
}
if (isNaN(interestRate) || interestRate < 0) {
errorMessageDiv.textContent = "Please enter a valid non-negative number for Periodic Interest Rate (e.g., 0.05 for 5%).";
return;
}
if (isNaN(numberOfPeriods) || numberOfPeriods <= 0) {
errorMessageDiv.textContent = "Please enter a valid positive number for Number of Periods.";
return;
}
var fv;
if (interestRate === 0) {
// Handle case where interest rate is zero
fv = periodicPayment * numberOfPeriods;
} else {
// Future Value formula for an ordinary annuity
fv = periodicPayment * (Math.pow(1 + interestRate, numberOfPeriods) – 1) / interestRate;
}
// Format the result to two decimal places and add currency symbol
annuityValueDiv.textContent = "$" + fv.toFixed(2);
}