An annuity is a financial product that pays out a stream of payments to the owner over a specified period. The most common application of annuity calculations is determining the regular payment amount required to either pay off a loan (loan amortization) or to accumulate a specific sum of money in the future. This calculator focuses on determining the fixed periodic payment (an ordinary annuity, where payments are made at the end of each period) needed to reach a certain present value or to amortize a loan.
The Formula
The formula to calculate the periodic payment (PMT) for an ordinary annuity, given the present value (PV), the periodic interest rate (r), and the number of periods (n), is derived from the present value of an ordinary annuity formula:
P = PV * [ r(1 + r)^n ] / [ (1 + r)^n – 1]
Where:
P = Periodic Payment Amount
PV = Present Value (the lump sum amount of the loan or investment at the beginning)
r = Periodic Interest Rate (Annual Interest Rate / Number of compounding periods per year)
n = Total Number of Periods (Number of years * Number of compounding periods per year)
How to Use This Calculator
Present Value (PV): Enter the total amount of the loan you need to repay, or the initial sum you have for an investment.
Annual Interest Rate (%): Input the annual interest rate for the loan or investment. The calculator will automatically convert this to a periodic rate.
Number of Periods (n): Enter the total number of payment periods. For example, if it's a 5-year loan with monthly payments, this would be 5 years * 12 months/year = 60 periods.
Click "Calculate Payment" to see the fixed amount you need to pay (or will receive) each period.
Use Cases
Loan Amortization: Calculate your fixed monthly mortgage, car loan, or personal loan payments.
Retirement Savings: Determine how much you need to save periodically to reach a specific retirement fund goal by a certain age (though this calculator uses present value as the target, it's conceptually related to future value savings goals).
Lease Payments: Estimate the fixed payments for a lease agreement.
Investment Payouts: Calculate the regular income you might receive from an annuity investment.
function calculateAnnuityPayment() {
var pv = parseFloat(document.getElementById("presentValue").value);
var annualRatePercent = parseFloat(document.getElementById("interestRate").value);
var n = parseInt(document.getElementById("numberOfPeriods").value);
var resultElement = document.getElementById("result").querySelector("span");
if (isNaN(pv) || isNaN(annualRatePercent) || isNaN(n) || pv <= 0 || annualRatePercent < 0 || n <= 0) {
resultElement.textContent = "Please enter valid positive numbers.";
return;
}
var r = annualRatePercent / 100; // Convert annual percentage to decimal rate
// For simplicity, this calculator assumes payments and compounding are aligned (e.g., monthly payments, monthly compounding)
// If periods are not annual, the interest rate 'r' would need to be adjusted per period (e.g., r = annualRatePercent / 100 / 12 for monthly)
// However, the input `numberOfPeriods` is already the total number of periods, so `r` here directly represents the rate per period if that's how it's used.
// A common interpretation is that `numberOfPeriods` represents the total payment cycles, and `r` is the rate *per cycle*.
// If annual rate and n periods (e.g. monthly payments for X years), then r should be annualRate/100/12 and n should be X*12.
// For this generic calculator, we assume 'r' as provided is the rate per period and 'n' is the number of periods.
var payment;
if (r === 0) { // Handle case where interest rate is 0
payment = pv / n;
} else {
var numerator = r * Math.pow(1 + r, n);
var denominator = Math.pow(1 + r, n) – 1;
payment = pv * (numerator / denominator);
}
if (isNaN(payment) || !isFinite(payment)) {
resultElement.textContent = "Calculation error. Check inputs.";
} else {
resultElement.textContent = "$" + payment.toFixed(2);
}
}