Present Value of Annuity Calculator with Discount Rate

Present Value of Annuity Calculator

Ordinary Annuity (End of Period) Annuity Due (Start of Period)

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Present Value:

Total Cash Payments:

Total Discount Applied:

Please ensure all fields are filled with positive values.

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What is the Present Value of an Annuity?

The Present Value (PV) of an annuity is a financial calculation that determines the current value of a series of future equal payments. This concept is fundamental in finance and accounting, as it helps individuals and businesses understand what a stream of future cash flows is worth today, given a specific Discount Rate.

The discount rate represents the "time value of money"—the idea that a dollar today is worth more than a dollar tomorrow because of its potential earning capacity. By applying this rate to future payments, we "discount" them back to their current value.

The Present Value Formula

The standard formula for an Ordinary Annuity (where payments are made at the end of each period) is:

PV = P * [(1 – (1 + r)^-n) / r]

• PV = Present Value
• P = Periodic Payment Amount
• r = Discount Rate per period (as a decimal)
• n = Total Number of Periods

Difference Between Ordinary Annuity and Annuity Due

When calculating the present value, the timing of the payment matters significantly:

• Ordinary Annuity: Payments are made at the end of each period (e.g., standard dividends or bond interest).
• Annuity Due: Payments are made at the beginning of each period (e.g., rent payments or insurance premiums). Because payments happen sooner, the present value of an annuity due is always higher than that of an ordinary annuity.

Practical Example

Imagine you are offered a structured settlement that pays you $5,000 every year for 10 years. You want to know if it is better to take the payments or a lump sum today. If the current market discount rate is 6%:

• Payment (P): $5,000
• Discount Rate (r): 0.06
• Periods (n): 10

Using the calculator, the Present Value would be approximately $36,800.44. If the lump sum offer today is $35,000, the annuity is technically more valuable. If the lump sum is $40,000, you might prefer taking the cash now.

function calculatePVA() { var payment = parseFloat(document.getElementById('paymentAmount').value); var ratePercent = parseFloat(document.getElementById('discountRate').value); var periods = parseFloat(document.getElementById('numberOfPeriods').value); var type = document.getElementById('annuityType').value; var errorDiv = document.getElementById('pva-error'); var resultDiv = document.getElementById('pva-result-container'); // Reset UI errorDiv.style.display = 'none'; resultDiv.style.display = 'none'; // Validation if (isNaN(payment) || isNaN(ratePercent) || isNaN(periods) || payment <= 0 || periods <= 0) { errorDiv.style.display = 'block'; return; } // Handle zero interest rate edge case var pv = 0; var r = ratePercent / 100; if (r === 0) { pv = payment * periods; } else { // Ordinary Annuity Formula: PV = P * [(1 – (1 + r)^-n) / r] pv = payment * ((1 – Math.pow(1 + r, -periods)) / r); // Adjustment for Annuity Due if (type === 'due') { pv = pv * (1 + r); } } var totalCash = payment * periods; var totalDiscount = totalCash – pv; // Display Results document.getElementById('resPV').innerText = '$' + pv.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resTotalPayments').innerText = '$' + totalCash.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resDiscount').innerText = '$' + totalDiscount.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); resultDiv.style.display = 'block'; }