Calculate the future value of a series of equal payments (annuity).
Per period
% (e.g., 5 for 5%)
(e.g., years, months)
Future Value of Annuity:
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Understanding Annuities and How to Calculate Their Future Value
An annuity is a financial product that pays out a stream of equal payments to an individual over a period of time. Annuities are commonly used for retirement planning, providing a steady income stream after a person stops working. They can be structured in various ways, but a fundamental calculation is determining the Future Value (FV) of these regular payments.
What is Future Value of an Annuity?
The Future Value of an annuity represents the total worth of a series of future payments, assuming each payment is reinvested at a specific rate of return. This calculation is crucial for understanding how much an investment will grow over time, considering the compounding effect of interest on each payment.
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]
Where:
FV is the Future Value of the annuity.
P is the amount of each periodic payment.
r is the interest rate per period.
n is the total number of periods.
If the interest rate (r) is zero, the formula simplifies to: FV = P * n
How the Calculator Works
This calculator takes three key inputs:
Periodic Payment Amount (P): The fixed amount paid at the end of each period.
Interest Rate per Period (r): The rate at which your investment grows, expressed as a percentage per period. For example, if you have an annual rate of 5% and payments are monthly, the rate per period would be 5%/12. However, this calculator assumes the rate provided is already per the payment period.
Number of Periods (n): The total count of payments to be made or received.
It then applies the future value of an ordinary annuity formula to compute the total projected value at the end of the term.
Use Cases for the Annuity Calculator
Retirement Planning: Estimate the future value of your regular savings contributions for retirement.
Investment Growth Projection: See how much your regular investments in stocks, bonds, or other instruments might be worth in the future.
Savings Goals: Determine the potential future value of saving a fixed amount monthly or yearly for a specific goal, like a down payment on a house or a child's education.
Loan Amortization (Inverse Use): While this calculator is for FV, understanding annuity calculations is foundational to understanding how loans are paid off over time.
By understanding the future value of your annuity, you can make more informed financial decisions and better plan for your long-term financial objectives.
Example Calculation:
Let's say you plan to invest $150 per month for 10 years, and you expect an average annual interest rate of 6%, compounded monthly.
Periodic Payment (P) = $150
Number of Periods (n) = 10 years * 12 months/year = 120 months
Interest Rate per Period (r) = 6% annual / 12 months/year = 0.5% monthly = 0.005
Using the formula: FV = 150 * [((1 + 0.005)^120 – 1) / 0.005]
FV = 150 * [((1.005)^120 – 1) / 0.005]
FV = 150 * [(1.81939673 – 1) / 0.005]
FV = 150 * [0.81939673 / 0.005]
FV = 150 * 163.879346
FV ≈ $24,581.90
So, after 10 years, your investment could grow to approximately $24,581.90.
function calculateAnnuity() {
var paymentAmountInput = document.getElementById("paymentAmount");
var interestRateInput = document.getElementById("interestRate");
var numberOfPeriodsInput = document.getElementById("numberOfPeriods");
var resultDiv = document.getElementById("result");
var paymentAmount = parseFloat(paymentAmountInput.value);
var interestRatePercent = parseFloat(interestRateInput.value);
var numberOfPeriods = parseFloat(numberOfPeriodsInput.value);
// Basic validation
if (isNaN(paymentAmount) || isNaN(interestRatePercent) || isNaN(numberOfPeriods) ||
paymentAmount <= 0 || numberOfPeriods <= 0) {
resultDiv.textContent = "Invalid input. Please enter positive numbers.";
resultDiv.style.color = "#dc3545"; // Error red
return;
}
var interestRate = interestRatePercent / 100; // Convert percentage to decimal
var futureValue;
if (interestRate === 0) {
futureValue = paymentAmount * numberOfPeriods;
} else {
// Future Value of an Ordinary Annuity Formula: FV = P * [((1 + r)^n – 1) / r]
futureValue = paymentAmount * (Math.pow((1 + interestRate), numberOfPeriods) – 1) / interestRate;
}
// Format the result to two decimal places
var formattedFutureValue = futureValue.toLocaleString(undefined, {
minimumFractionDigits: 2,
maximumFractionDigits: 2
});
resultDiv.textContent = "$" + formattedFutureValue;
resultDiv.style.color = "#28a745"; // Success Green
}