An annuity is a series of equal payments made at regular intervals. Annuity payments are commonly used in financial planning, such as for retirement income, loan amortization, or structured settlements. This calculator helps you determine the size of each regular payment (annuity payment) needed to reach a specific future value or to repay a present value over a set period with a given interest rate.
This calculator specifically focuses on the Present Value of an Ordinary Annuity, where payments are made at the end of each period. The formula used is:
PV = PMT * [1 - (1 + r)^-n] / r
Where:
PV is the Present Value (the total amount you have now or need to borrow).
PMT is the Annuity Payment (the amount you need to calculate).
r is the interest rate per period.
n is the total number of periods.
To find the PMT, we rearrange the formula:
PMT = PV / ([1 - (1 + r)^-n] / r)
Or, more simply:
PMT = PV * r / [1 - (1 + r)^-n]
How to Use This Calculator:
Present Value (PV): Enter the lump sum amount you have today that you want to receive payments from, or the total amount of a loan you are taking out.
Annual Interest Rate (%): Input the annual interest rate. The calculator will automatically convert this to a periodic rate if your periods are not annual. For simplicity in this calculator, we assume the 'Number of Periods' and the 'Interest Rate' are aligned (e.g., if you have years, the rate is annual; if you have months, you'd typically adjust the rate to monthly). For this specific implementation, we use the annual rate directly and assume the number of periods is also in years for simplicity, or you should input the periodic rate and number of periods accordingly. Important: For more precise calculations with different compounding and payment frequencies (e.g., monthly payments on an annual rate), you would need to adjust the rate (divide annual rate by 12) and the number of periods (multiply years by 12).
Number of Periods: Enter the total number of payment periods (e.g., years, months).
Click "Calculate Annuity Payment".
The result will show the fixed payment amount you would receive or need to make for each period to amortize the present value over the specified number of periods at the given interest rate.
Example:
Imagine you have $200,000 today (PV) that you want to grow into a retirement fund through a series of equal annual payments over 20 years (n), earning an average annual interest rate of 7% (r).
PV = $200,000
Annual Interest Rate = 7%
Number of Periods = 20 years
Using the calculator with these inputs will provide the size of each annual payment.
function calculateAnnuityPayment() {
var pv = parseFloat(document.getElementById("presentValue").value);
var annualInterestRate = parseFloat(document.getElementById("interestRate").value);
var numberOfPeriods = parseFloat(document.getElementById("numberOfPeriods").value);
var resultDiv = document.getElementById("result");
var resultSpan = resultDiv.querySelector("span");
// Basic validation
if (isNaN(pv) || pv <= 0 || isNaN(annualInterestRate) || annualInterestRate < 0 || isNaN(numberOfPeriods) || numberOfPeriods <= 0) {
alert("Please enter valid positive numbers for all fields.");
resultDiv.style.display = 'none';
return;
}
// For simplicity, assuming the interest rate and number of periods are aligned (e.g., both annual).
// In real-world scenarios, you'd often need to adjust rate and periods for monthly/quarterly calculations.
var periodicInterestRate = annualInterestRate / 100; // Convert percentage to decimal
// Formula for PMT (Annuity Payment) from PV: PMT = PV * r / [1 – (1 + r)^-n]
// Ensure the denominator is not zero
var denominator = 1 – Math.pow(1 + periodicInterestRate, -numberOfPeriods);
if (denominator === 0) {
alert("Calculation error: Denominator is zero. Please check your inputs.");
resultDiv.style.display = 'none';
return;
}
var pmt = pv * periodicInterestRate / denominator;
// Format the output to two decimal places
resultSpan.textContent = "$" + pmt.toFixed(2);
resultDiv.style.display = 'block';
}