Ordinary Annuity (payments at end of period)
Annuity Due (payments at beginning of period)
Annuity Present Value
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Understanding Annuity Present Value
The Present Value (PV) of an Annuity is the current worth of a series of future equal payments, discounted at a specific interest rate. In simpler terms, it tells you how much a stream of future payments is worth today.
This concept is crucial in finance for valuing investments, understanding loan payoffs, and making informed financial decisions. For example, if someone offers you a stream of payments over several years, the annuity present value helps you determine if that stream is a good deal compared to receiving a lump sum today.
The Formula
The formula for the Present Value of an Annuity depends on whether the payments occur at the end of each period (Ordinary Annuity) or at the beginning (Annuity Due).
1. Ordinary Annuity (Payments at the end of each period)
The formula is:
PV = P * [1 - (1 + r)^-n] / r
Where:
PV = Present Value of the Annuity
P = Periodic Payment Amount (the amount paid each period)
r = Periodic Interest Rate (the interest rate per period, expressed as a decimal)
n = Number of Periods (the total number of payments)
2. Annuity Due (Payments at the beginning of each period)
The formula is:
PV = P * [1 - (1 + r)^-n] / r * (1 + r)
Notice that the formula for an annuity due is simply the formula for an ordinary annuity multiplied by (1 + r). This is because each payment in an annuity due is received one period earlier, thus earning an extra period of interest.
How the Calculator Works
Our calculator takes the following inputs:
Periodic Payment Amount (P): The fixed amount paid in each installment.
Periodic Interest Rate (r): The interest rate applied per payment period. This is usually expressed as a percentage and needs to be converted to a decimal for calculation (e.g., 5% becomes 0.05).
Number of Periods (n): The total count of payments to be made.
Annuity Type: Whether payments are made at the end of the period (Ordinary) or at the beginning (Annuity Due).
It then applies the appropriate formula based on your selections to compute and display the Present Value of the annuity.
Use Cases
Investment Valuation: Determining the current worth of a long-term investment that pays out over time.
Retirement Planning: Estimating the present value of future pension payments or retirement income streams.
Lump Sum vs. Payments: Deciding whether to accept a lump sum payment today or a series of future payments by comparing the lump sum to the calculated annuity present value.
Lease and Rental Agreements: Valuing long-term leases or rental income streams.
Legal Settlements: Calculating the present value of structured legal settlements.
function calculateAnnuityPV() {
var paymentAmount = parseFloat(document.getElementById("paymentAmount").value);
var interestRatePercent = parseFloat(document.getElementById("interestRate").value);
var numberOfPeriods = parseInt(document.getElementById("numberOfPeriods").value);
var annuityType = document.getElementById("annuityType").value;
var resultElement = document.getElementById("result-value");
resultElement.textContent = "–"; // Reset previous result
// Input validation
if (isNaN(paymentAmount) || paymentAmount <= 0) {
alert("Please enter a valid positive number for the Periodic Payment Amount.");
return;
}
if (isNaN(interestRatePercent) || interestRatePercent < 0) {
alert("Please enter a valid non-negative number for the Periodic Interest Rate.");
return;
}
if (isNaN(numberOfPeriods) || numberOfPeriods <= 0) {
alert("Please enter a valid positive integer for the Number of Periods.");
return;
}
var interestRateDecimal = interestRatePercent / 100;
var pv;
// Handle the case where interest rate is 0 to avoid division by zero
if (interestRateDecimal === 0) {
pv = paymentAmount * numberOfPeriods;
} else {
// Calculate the common part of the formula: [1 – (1 + r)^-n] / r
var discountFactor = (1 – Math.pow(1 + interestRateDecimal, -numberOfPeriods)) / interestRateDecimal;
if (annuityType === "ordinary") {
pv = paymentAmount * discountFactor;
} else { // annuityType === "due"
pv = paymentAmount * discountFactor * (1 + interestRateDecimal);
}
}
// Format the result to two decimal places
resultElement.textContent = "$" + pv.toFixed(2);
}