Understanding Annuities and the Future Value Formula
An annuity is a series of equal payments made at regular intervals. These can be used for various financial goals, such as saving for retirement, planning for future expenses, or accumulating funds for a specific purchase. The core principle behind an annuity is that your money grows over time, especially when interest is involved.
This calculator helps you determine the Future Value (FV) of an ordinary annuity. An ordinary annuity is one where payments are made at the *end* of each period. The future value tells you how much your series of payments will be worth at a specific point in the future, considering the compounding interest earned.
The Future Value of an Ordinary Annuity Formula
FV = P * [ ((1 + r)^n – 1) / r ]
Where:
FV is the Future Value of the annuity.
P is the periodic payment amount (the amount you pay each period).
r is the periodic interest rate (the interest rate per period, expressed as a decimal).
n is the number of periods.
How the Calculator Works
Our calculator takes three inputs:
Periodic Payment Amount (P): The fixed amount of money you will deposit or invest at the end of each period (e.g., $100 per month).
Periodic Interest Rate (r): The interest rate applied to your investment per period. This must be entered as a decimal. For example, an annual rate of 5% compounded monthly would mean a periodic rate of (5% / 12) = 0.05 / 12, but for simplicity, if your rate is already compounded per period, enter it directly (e.g., 0.05 for 5% per period).
Number of Periods (n): The total number of payment periods over which the annuity will run (e.g., 120 months for 10 years if payments are monthly).
By plugging these values into the formula, the calculator computes the total accumulated amount you will have at the end of the specified number of periods, including all your payments and the compounded interest.
Use Cases for an Annuity FV Calculator:
Retirement Planning: Estimating how much your regular savings contributions will grow to by your retirement date.
Saving for Goals: Calculating the future value of regular savings for a down payment on a house, a new car, or a child's education.
Investment Projections: Understanding the potential growth of a systematic investment plan.
Evaluating Financial Products: Comparing the potential returns of different investment or savings products that offer regular payments.
Example: Suppose you plan to save $200 at the end of each month for 5 years (60 months), and your investment earns a monthly interest rate of 0.5% (0.005 as a decimal). Using the calculator:
Periodic Payment (P): $200
Periodic Interest Rate (r): 0.005
Number of Periods (n): 60
The calculator will compute the future value, showing you the total sum accumulated after 5 years.
function calculateAnnuity() {
var periodicPayment = parseFloat(document.getElementById("periodicPayment").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var numberOfPeriods = parseFloat(document.getElementById("numberOfPeriods").value);
var resultElement = document.getElementById("result").querySelector("span");
if (isNaN(periodicPayment) || isNaN(interestRate) || isNaN(numberOfPeriods)) {
resultElement.textContent = "Invalid input. Please enter valid numbers.";
return;
}
if (periodicPayment < 0 || interestRate < 0 || numberOfPeriods <= 0) {
resultElement.textContent = "Inputs must be positive, and periods must be greater than zero.";
return;
}
var futureValue;
if (interestRate === 0) {
futureValue = periodicPayment * numberOfPeriods;
} else {
futureValue = periodicPayment * (Math.pow(1 + interestRate, numberOfPeriods) – 1) / interestRate;
}
// Format to two decimal places for currency display
resultElement.textContent = "$" + futureValue.toFixed(2);
}