Calculate the Present Value (PV) of an annuity stream by applying a specific discount rate. Determine the current worth of future periodic payments.
Annually (Once a year)
Semi-Annually (Twice a year)
Quarterly (4 times a year)
Monthly (12 times a year)
Bi-Weekly (26 times a year)
Weekly (52 times a year)
Ordinary Annuity (Payment at End of Period)
Annuity Due (Payment at Beginning of Period)
Please enter valid numeric values for Payment, Rate, and Duration.
Calculation Results
Present Value (PV):$0.00
Total Number of Payments:0
Total Cash Flow (Undiscounted):$0.00
Discount Effect (Interest/Time Value):$0.00
Understanding the Discount Rate Annuity Calculator
In finance and actuarial science, the value of money changes over time. A dollar received today is worth more than a dollar received in the future due to its potential earning capacity. This tool helps you determine the Present Value (PV) of a series of equal future payments (an annuity) by applying a specific discount rate.
Why use a Discount Rate?
The discount rate essentially reverses the interest rate. While an interest rate tells you how much money will grow, a discount rate tells you how much future money is worth right now. This is critical for:
Settlements: determining the lump sum value of a structured settlement.
Pension Valuation: calculating the current obligation of future pension payouts.
Investment Analysis: comparing a lump sum investment against a stream of rental income or dividends.
Ordinary Annuity vs. Annuity Due
The timing of the payments significantly affects the calculation:
Ordinary Annuity: Payments are made at the end of each period (e.g., standard mortgage payments or bond coupons).
Annuity Due: Payments are made at the beginning of each period (e.g., rent payments or lease agreements). Annuity due values are always higher because the money is received sooner.
The Math Behind the Calculation
The calculator uses the following logic to derive the Present Value.
Variables: PMT = Periodic Payment Amount
r = Periodic Discount Rate (Annual Rate / Frequency)
n = Total Number of Periods (Years × Frequency)
Annuity Due Formula:
PV = PMT × [ (1 – (1 + r)^-n) / r ] × (1 + r)
Example Calculation
Imagine you are offered a structured settlement that pays $1,000 monthly for 10 years. You want to know what this stream of income is worth today, assuming a discount rate of 5%.
Total Periods (n): 10 years × 12 months = 120 payments.
Periodic Rate (r): 5% ÷ 12 = 0.4167% per month.
Calculation: Using the Ordinary Annuity formula, the Present Value would be approximately $94,281.35.
Comparison: The total raw cash collected is $120,000 ($1,000 × 120), meaning the "cost" of waiting for the money (the discount effect) is roughly $25,718.
function calculatePresentValue() {
// 1. Get DOM elements
var paymentInput = document.getElementById('periodicPayment');
var rateInput = document.getElementById('annualDiscountRate');
var yearsInput = document.getElementById('durationYears');
var frequencySelect = document.getElementById('paymentFrequency');
var typeSelect = document.getElementById('annuityType');
var errorMsg = document.getElementById('error-message');
var resultsArea = document.getElementById('results-area');
// 2. Parse values
var P = parseFloat(paymentInput.value);
var annualRate = parseFloat(rateInput.value);
var years = parseFloat(yearsInput.value);
var freq = parseInt(frequencySelect.value);
var type = typeSelect.value;
// 3. Validation
if (isNaN(P) || isNaN(annualRate) || isNaN(years) || P < 0 || annualRate < 0 || years <= 0) {
errorMsg.style.display = 'block';
resultsArea.style.display = 'none';
return;
}
errorMsg.style.display = 'none';
// 4. Calculation Logic
var r = (annualRate / 100) / freq; // Periodic interest rate
var n = years * freq; // Total number of periods
var pv = 0;
// Handle 0% interest rate edge case
if (r === 0) {
pv = P * n;
} else {
// Standard PV formula for Ordinary Annuity
// PV = P * [ (1 – (1+r)^-n) / r ]
var discountFactor = (1 – Math.pow((1 + r), -n)) / r;
pv = P * discountFactor;
// Adjustment for Annuity Due (Beginning of period)
if (type === 'due') {
pv = pv * (1 + r);
}
}
var totalCash = P * n;
var discountEffect = totalCash – pv;
// 5. Update DOM with Results
document.getElementById('resultPV').innerText = formatCurrency(pv);
document.getElementById('resultTotalPayments').innerText = Math.round(n);
document.getElementById('resultTotalCash').innerText = formatCurrency(totalCash);
document.getElementById('resultDiscountEffect').innerText = formatCurrency(discountEffect);
resultsArea.style.display = 'block';
}
function formatCurrency(num) {
return '$' + num.toFixed(2).replace(/\d(?=(\d{3})+\.)/g, '$&,');
}