TI Financial Calculator: Future Value of an Ordinary Annuity
Calculate the future value of a series of equal payments made at regular intervals.
Understanding the Future Value of an Ordinary Annuity
The Future Value (FV) of an Ordinary Annuity calculator helps you project the total worth of a sequence of equal payments over time, assuming each payment earns compound interest at a constant rate. An "ordinary annuity" means that payments are made at the end of each period. This is a fundamental concept in finance, useful for planning savings, investments, and loan payoffs.
The Formula
The mathematical formula used to calculate the Future Value of an Ordinary Annuity is:
FV = P * [((1 + r)^n - 1) / r]
Where:
FV is the Future Value of the annuity.
P is the periodic payment amount (the amount paid each period).
r is the periodic interest rate (expressed as a decimal). For example, 5% is entered as 0.05.
n is the total number of periods over which payments are made.
How it Works
Each payment made into the annuity grows over time due to compound interest. The formula essentially sums up the future value of each individual payment, taking into account the time it has to earn interest.
The term (1 + r)^n represents the growth factor of a single sum after n periods at rate r.
Subtracting 1 adjusts this for the fact that we are dealing with a series of payments, not just one lump sum.
Dividing by r scales the result correctly to represent the annuity.
Finally, multiplying by P scales the entire amount by the size of each periodic payment.
Use Cases
This calculator is invaluable for:
Retirement Planning: Estimating the future value of regular contributions to a retirement account (like a 401(k) or IRA).
Savings Goals: Projecting how much a savings plan (e.g., saving for a down payment, a car, or education) will grow over time.
Investment Projections: Forecasting the potential growth of a systematic investment plan.
Loan Payoff Analysis: Understanding how consistently paying extra on a loan can affect the total amount paid and the time to payoff (though this calculator focuses on growth, not amortization).
Example Calculation
Let's say you plan to deposit $100 at the end of each month into a savings account that earns 6% annual interest, compounded monthly. This means:
So, after 60 months, your savings would grow to approximately $6,977.00.
function calculateFVAPeriodic() {
var paymentAmount = parseFloat(document.getElementById("paymentAmount").value);
var interestRate = parseFloat(document.getElementById("interestRate").value);
var numberOfPeriods = parseFloat(document.getElementById("numberOfPeriods").value);
var resultDiv = document.getElementById("result");
// Input validation
if (isNaN(paymentAmount) || paymentAmount <= 0) {
resultDiv.innerHTML = "Please enter a valid Periodic Payment Amount.";
return;
}
if (isNaN(interestRate) || interestRate < 0) {
resultDiv.innerHTML = "Please enter a valid Periodic Interest Rate (decimal format).";
return;
}
if (isNaN(numberOfPeriods) || numberOfPeriods <= 0) {
resultDiv.innerHTML = "Please enter a valid Number of Periods.";
return;
}
var fv;
// Handle the special case where interest rate is 0
if (interestRate === 0) {
fv = paymentAmount * numberOfPeriods;
} else {
fv = paymentAmount * (Math.pow((1 + interestRate), numberOfPeriods) – 1) / interestRate;
}
// Format the result to two decimal places
var formattedFV = fv.toFixed(2);
resultDiv.innerHTML = "$" + formattedFV + " (Total Future Value)";
}