Monthly Annuity Formula Calculator

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Monthly Annuity Formula Calculator

End of Month (Ordinary) Beginning of Month (Due)

Calculation Results

Present Value (PV): –
Future Value (FV): –
Total Contributions: –
function calculateMonthlyAnnuity() { var P = parseFloat(document.getElementById("monthlyPayment").value); var annualR = parseFloat(document.getElementById("growthRate").value); var t = parseFloat(document.getElementById("totalYears").value); var type = document.getElementById("paymentTiming").value; if (isNaN(P) || isNaN(annualR) || isNaN(t) || P <= 0 || t <= 0) { alert("Please enter valid positive numbers for all fields."); return; } var r = (annualR / 100) / 12; var n = t * 12; var pv = 0; var fv = 0; if (r === 0) { pv = P * n; fv = P * n; } else { // Ordinary Annuity (End of Period) pv = P * ((1 – Math.pow(1 + r, -n)) / r); fv = P * ((Math.pow(1 + r, n) – 1) / r); // Adjustment for Annuity Due (Beginning of Period) if (type === "start") { pv = pv * (1 + r); fv = fv * (1 + r); } } document.getElementById("pvDisplay").innerText = "$" + pv.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById("fvDisplay").innerText = "$" + fv.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById("totalInputDisplay").innerText = "$" + (P * n).toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById("annuityResults").style.display = "block"; }

Understanding the Monthly Annuity Formula

A monthly annuity represents a sequence of equal payments made at regular monthly intervals. This financial concept is critical for retirement planning, structured settlements, and determining the worth of recurring cash flows. Using the monthly annuity formula allows you to determine how much a series of future payments is worth today (Present Value) or what those payments will grow to over time (Future Value).

The Mathematics Behind the Calculation

The calculation depends on whether payments occur at the start or the end of each month. The primary formula used for an Ordinary Annuity (payments at the end of the month) is:

PV = P × [(1 – (1 + r)-n) / r]

Where:

  • P: Monthly payment amount
  • r: Periodic monthly rate (Annual Rate ÷ 12)
  • n: Total number of monthly periods (Years × 12)

Ordinary Annuity vs. Annuity Due

The timing of the payment significantly impacts the total value due to the effect of compounding:

  • • Ordinary Annuity: Payments are made at the end of each period. This is common for most consumer loans and insurance payments.
  • • Annuity Due: Payments are made at the beginning of each period. Because the money is deposited earlier, it has more time to accrue interest, resulting in a higher total value.

Practical Example

Suppose you are scheduled to receive a monthly payment of $1,000 for 5 years. If the prevailing annual growth rate is 5%, here is how the values break down:

Metric Value
Total Monthly Payments (n) 60
Monthly Interest Rate (r) 0.4167%
Present Value (PV) $53,004.53
Future Value (FV) $68,006.08

Why Present Value Matters

The Present Value (PV) tells you what a future stream of income is worth in today's dollars. This is essential when deciding between taking a lump-sum payment or receiving a monthly annuity. If the lump sum offered is higher than the PV calculated here, the lump sum might be the more mathematically sound choice, assuming equal risk levels.

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