Determine the expected time required to repay the principal of a loan or bond, accounting for amortization and prepayments.
The initial face value or current loan balance.
Please enter a positive principal amount.
The annual interest rate applied to the balance.
Enter a valid positive interest rate.
The total remaining term of the loan or bond.
Enter a term between 1 and 50 years.
Fully Amortizing (Mortgage/Loan)
Bullet / Interest Only (Bond)
Select how the principal is repaid over time.
Estimated annual % of principal paid early (0 for none).
Enter a valid prepayment rate (0-20%).
Weighted Average Life (WAL)
0.00 Years
Formula: Σ (Principal Paid × Time) / Total Principal
Total Principal Repaid$0.00
Total Interest Cost$0.00
Stated Maturity0 Years
Est. Monthly Payment$0.00
Principal Repayment Profile
Blue area represents Principal Balance over time.
Annual Cash Flow Summary (First 10 Years)
Year
Principal Paid
Interest Paid
Remaining Balance
Showing annual aggregation. Full calculation uses monthly periods.
What is Weighted Average Life (WAL) Calculation?
In the world of fixed-income securities, loans, and mortgage-backed securities (MBS), the maturity date rarely tells the whole story. The Weighted Average Life calculation is a critical financial metric that measures the average time it takes for every dollar of principal to be repaid. Unlike a simple maturity date, which only indicates when the final payment is due, the weighted average life (WAL) accounts for the timing of all principal payments—whether they occur through scheduled amortization or prepayments.
Investors and portfolio managers use the weighted average life calculation to assess credit risk and interest rate sensitivity. A shorter WAL implies that the principal is returned faster, reducing the exposure to long-term market volatility. Conversely, a longer WAL suggests the capital is tied up for a longer duration, potentially offering higher yields but with greater risk.
Weighted Average Life Calculation Formula and Explanation
The core concept behind the weighted average life calculation is "weighting" time by the amount of principal repaid. The formula sums up the product of the time (in years) and the principal amount paid at that time, then divides by the total principal balance.
WAL Formula: WAL = Σ ( Pi × ti ) / Ptotal
Variable
Meaning
Unit
Typical Context
Pi
Principal repayment amount at time i
Currency ($)
Monthly/Annual portion
ti
Time elapsed since origination
Years
Payment date timing
Ptotal
Total Principal (Face Value)
Currency ($)
Original loan amount
WAL
Weighted Average Life
Years
Resulting metric
Practical Examples of Weighted Average Life Calculation
Example 1: The Bullet Bond
Consider a corporate bond with a $100,000 face value, a 5-year maturity, and no amortization (interest-only payments). Since 100% of the principal is repaid exactly at year 5:
Principal Payment at Year 5: $100,000
Calculation: ($100,000 × 5) / $100,000 = 5.0 Years
For bullet bonds, the WAL equals the maturity.
Example 2: The Amortizing Mortgage
Consider a $100,000 mortgage with a 30-year term and a 5% interest rate. The borrower pays principal every single month. In the early years, payments are mostly interest. In later years, payments are mostly principal.
A significant portion of principal is paid in years 20-30.
However, small principal payments start immediately at month 1.
Result: The weighted average life calculation will yield significantly less than 30 years—typically around 20 to 22 years for a standard schedule without prepayments. If the borrower prepays, the WAL drops further.
How to Use This Weighted Average Life Calculator
This tool is designed to bridge the gap between simple maturity and complex cash flow analysis. Follow these steps:
Enter Principal: Input the current face value of the bond or loan balance.
Set Interest Rate: Enter the annual coupon or note rate. This determines how much of your payment goes to interest vs. principal.
Select Term: Input the number of years until the final maturity date.
Choose Structure: Select "Fully Amortizing" for mortgages/loans or "Bullet" for standard bonds.
Adjust Prepayments (CPR): If analyzing a mortgage-backed security, input a CPR (Constant Prepayment Rate) to see how early repayments shorten the weighted average life calculation.
Key Factors That Affect Weighted Average Life
Several variables can drastically shift the outcome of a weighted average life calculation:
Amortization Schedule: Loans that pay principal gradually (amortizing) always have a WAL shorter than their maturity. Bullet loans have a WAL equal to maturity.
Interest Rate: In a fixed-payment loan, a higher interest rate means a smaller portion of the early payments goes to principal, slightly extending the WAL compared to a lower-rate loan.
Prepayment Speed (CPR/PSA): This is the single biggest factor for MBS. High prepayment rates (due to refinancing incentives) drastically shorten the WAL.
Sinking Funds: Bonds with sinking funds require the issuer to retire a portion of debt periodically, lowering the WAL.
Call Provisions: If a bond is callable, the "Yield to Worst" or "WAL to Call" might be a more relevant metric than WAL to maturity.
Payment Frequency: Monthly payments return principal slightly faster than semi-annual or annual payments, marginally reducing the WAL.
Frequently Asked Questions (FAQ)
1. Is Weighted Average Life the same as Duration?
No. While related, they are distinct. WAL only considers principal repayments. Duration (Macaulay or Modified) considers the timing of both interest and principal payments and is used primarily to measure interest rate sensitivity.
2. Why is WAL important for Mortgage-Backed Securities?
MBS investors face "contraction risk" (loans paid off too early) and "extension risk" (loans paid off too slowly). The weighted average life calculation helps quantify these risks under different prepayment scenarios.
3. Can WAL be longer than Maturity?
No. Since WAL is an average of the time required to pay principal, and all principal must be paid by maturity, the WAL cannot exceed the final maturity date.
4. How does a 0% interest rate affect WAL?
If interest is 0%, an amortizing loan pays principal linearly. For a term of $T$ years, the WAL would be exactly $T/2$ (assuming continuous linear payment) or close to it.
5. What is a "Bullet" loan?
A bullet loan requires interest-only payments for the life of the loan, with the entire principal due at the end. In this case, WAL = Maturity.
6. Does inflation affect the calculation?
Not directly. The weighted average life calculation is based on nominal cash flows defined by the contract, not real (inflation-adjusted) values.
7. What is CPR in this context?
CPR stands for Constant Prepayment Rate. It is an annualized percentage of the existing loan pool that is expected to be paid off early. A higher CPR results in a lower WAL.
8. Why do we divide by Total Principal?
We divide to normalize the result. The sum of (Principal × Time) gives "Dollar-Years." Dividing by Dollars leaves us with "Years," which is the unit of Weighted Average Life.
// GLOBAL VARIABLES
var principalInput = document.getElementById("principalInput");
var rateInput = document.getElementById("rateInput");
var termInput = document.getElementById("termInput");
var amortizationSelect = document.getElementById("amortizationType");
var prepaymentInput = document.getElementById("prepaymentInput");
var chartInstance = null; // We will use raw canvas, so this is just a placeholder variable if needed logic requires it.
// INITIALIZATION
window.onload = function() {
calculateWAL();
};
// VALIDATION HELPER
function validateInput(el) {
var val = parseFloat(el.value);
var errId = "";
if (el.id === "principalInput") errId = "err-principal";
if (el.id === "rateInput") errId = "err-rate";
if (el.id === "termInput") errId = "err-term";
if (el.id === "prepaymentInput") errId = "err-prepay";
var errEl = document.getElementById(errId);
if (isNaN(val) || val < 0) {
if (errEl) errEl.style.display = "block";
} else {
if (errEl) errEl.style.display = "none";
calculateWAL(); // Real-time update
}
}
// TOGGLE PREPAYMENT VISIBILITY
function togglePrepayment() {
var type = amortizationSelect.value;
var group = document.getElementById("prepaymentGroup");
if (type === "bullet") {
group.style.display = "none";
prepaymentInput.value = 0;
} else {
group.style.display = "block";
}
calculateWAL();
}
function resetCalculator() {
principalInput.value = 100000;
rateInput.value = 5.5;
termInput.value = 30;
amortizationSelect.value = "amortizing";
prepaymentInput.value = 0;
document.getElementById("prepaymentGroup").style.display = "block";
// Hide errors
var errs = document.querySelectorAll(".error-msg");
for (var i = 0; i < errs.length; i++) {
errs[i].style.display = "none";
}
calculateWAL();
}
// CORE CALCULATION LOGIC
function calculateWAL() {
var P = parseFloat(principalInput.value);
var r_annual = parseFloat(rateInput.value);
var years = parseFloat(termInput.value);
var type = amortizationSelect.value;
var cpr = parseFloat(prepaymentInput.value);
if (isNaN(P) || isNaN(r_annual) || isNaN(years) || P <= 0 || years <= 0) {
return; // invalid state
}
if (isNaN(cpr)) cpr = 0;
// Constants
var r_monthly = r_annual / 100 / 12;
var total_months = Math.ceil(years * 12);
// Single Monthly Mortality (SMM) from CPR
// Formula: SMM = 1 – (1 – CPR)^1/12
var smm = 1 – Math.pow((1 – cpr/100), 1/12);
var balance = P;
var totalPrincipalWeightedTime = 0;
var totalPrincipalPaid = 0;
var totalInterestPaid = 0;
var historyPrincipal = []; // For chart
var historyBalance = []; // For chart
var tableData = []; // For table
// Calculate fixed monthly payment if amortizing
var fixed_pmt = 0;
if (type === "amortizing") {
if (r_monthly === 0) {
fixed_pmt = P / total_months;
} else {
fixed_pmt = P * (r_monthly * Math.pow(1 + r_monthly, total_months)) / (Math.pow(1 + r_monthly, total_months) – 1);
}
}
// Loop through months
for (var m = 1; m balance) scheduledPrincipal = balance;
}
// Prepayment Logic
// Prepay is calculated on balance AFTER scheduled principal (Standard Model)
// or on opening balance. Let's use opening balance minus scheduled principal to be standard.
var unscheduledPrincipal = 0;
if (type === "amortizing" && balance – scheduledPrincipal > 0) {
unscheduledPrincipal = (balance – scheduledPrincipal) * smm;
}
var totalPrincipalThisMonth = scheduledPrincipal + unscheduledPrincipal;
if (totalPrincipalThisMonth > balance) totalPrincipalThisMonth = balance;
// Update Accumulators
// Time weight = m / 12 (years)
var timeInYears = m / 12;
totalPrincipalWeightedTime += totalPrincipalThisMonth * timeInYears;
totalPrincipalPaid += totalPrincipalThisMonth;
totalInterestPaid += interest;
balance -= totalPrincipalThisMonth;
// Store data for Chart/Table (Aggregate annually for table, keep some monthly for chart)
if (m % 12 === 0 || m === total_months) {
tableData.push({
year: Math.ceil(m / 12),
pPaid: totalPrincipalPaid, // cumulative logic for simplified table handling later
iPaid: totalInterestPaid,
bal: balance
});
}
// For chart, we just need points roughly every year or key intervals to keep it simple without libraries
if (m % Math.ceil(total_months/20) === 0 || m === total_months || m === 1) {
historyBalance.push({t: timeInYears, b: balance});
}
if (balance <= 0.01) break; // Loan paid off
}
// Final WAL Calc
var wal = totalPrincipalWeightedTime / P;
// Sanity Check
if (wal < 0) wal = 0;
// Render Outputs
document.getElementById("resultsSection").style.display = "block";
document.getElementById("walResult").innerText = wal.toFixed(2) + " Years";
document.getElementById("resPrincipal").innerText = "$" + P.toLocaleString();
document.getElementById("resInterest").innerText = "$" + totalInterestPaid.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById("resMaturity").innerText = years + " Years";
var displayPmt = (type === "bullet") ? (P * r_monthly) : fixed_pmt;
document.getElementById("resPayment").innerText = "$" + displayPmt.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + ((type === "bullet") ? " (Interest Only)" : "");
drawChart(historyBalance, P, years);
updateTable(tableData, P);
}
// TABLE GENERATION
function updateTable(data, originalPrincipal) {
var tbody = document.getElementById("scheduleTable").querySelector("tbody");
tbody.innerHTML = "";
var prevPP = 0;
var prevIP = 0;
// Limit to first 10 years for brevity in single file, or all if short
var limit = Math.min(data.length, 10);
for (var i = 0; i < limit; i++) {
var row = data[i];
// De-cumulate for annual display
var annualPrincipal = row.pPaid – prevPP;
var annualInterest = row.iPaid – prevIP;
prevPP = row.pPaid;
prevIP = row.iPaid;
var tr = document.createElement("tr");
tr.innerHTML =
"