# Weighted-average life Canonical: https://web4.xpay.bi/en/wiki/wp-en-15646748/ Language: en Published: 2026-10-29T22:19:03.710Z Updated: 2026-10-29T22:19:03.710Z In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life, is the weighted average of the times of the principal repayments: it's the average time until a dollar of principal is repaid. ## Key facts ## Overview In finance, the weighted-average life (WAL) of an amortizing loan or amortizing bond, also called average life, is the weighted average of the times of the principal repayments: it's the average time until a dollar of principal is repaid. In a formula, WAL = ∑ i = 1 n P i P t i , \{\\displaystyle \{\\text\{WAL\}\}=\\sum \_\{i=1\}^\{n\}\{\\frac \{P\_\{i\}\}\{P\}\}t\_\{i\},\} where: P \{\\displaystyle P\} is the (total) principal, P i \{\\displaystyle P\_\{i\}\} ## WAL of classes of loans In loans that allow prepayment, the WAL cannot be computed from the amortization schedule alone; one must also make assumptions about the prepayment and default behavior, and the quoted WAL will be an estimate. The WAL is usually computed from a single cash-flow sequence. Occasionally, a simulated average life may be computed from multiple cash-flow scenarios, such as those from an option-adjusted spread model. ## Related concepts WAL should not be confused with the following distinct concepts: Bond duration Bond duration is the weighted-average time to receive the discounted present values of all the cash flows (including both principal and interest), while WAL is the weighted-average time to receive simply the principal payments (not including interest, and not discounting). For an amortizing loan with equal payments, the WAL will be higher than the duration, as the early payments are weighted towards interest, while the later payments are weighted towards principal, and further, taking present value (in duration) discounts the later payments. Time until 50% of the principal has been repaid WAL is a mean, while "50% of the principal repaid" is a median; see difference between mean and median. Since principal outstanding is a concave function (of time) for a flat payment amortizing loan, less than half the principal will have been paid off at the WAL. Intuitively, this is because most of the principal repayment happens at the end. Formally, the distribution of repayments has negative skew: the small principal repayments at the beginning drag down the WAL (mean) more than they reduce the median. Weighted-average maturity (WAM) WAM is an average of the maturity dates of multiple loans, not an average of principal repayments. ## Applications WAL is a measure that can be useful in credit risk analysis on fixed income securities, bearing in mind that the main credit risk of a loan is the risk of loss of principal. All else equal, a bond with principal outstanding longer (i.e., longer WAL) has greater credit risk than a bond with shorter WAL. In particular, WAL is often used as the basis for yield comparisons in I-spread calculations. WAL should not be used to estimate a bond's price-sensitivity to interest-rate fluctuations, as WAL includes only the principal cash flows, omitting the interest payments. Instead, one should use bond duration, which incorporates all the cash flows. ## Examples The WAL of a bullet loan (non-amortizing) is exactly the tenor, as the principal is repaid precisely at maturity. On a 30-year amortizing loan, paying equal amounts monthly, one has the following WALs, for the given annual interest rates (and corresponding monthly payments per $100,000 principal balance, calculated via an amortization calculator and the formulas below relating amortized payments, total interest, and WAL): Note that as the interest rate increases, WAL increases, since the principal payments become increasingly back-loaded. WAL is independent of the principal balance, though payments and total interest are proportional to principal. For a coupon of 0%, where the principal amortizes linearly, the WAL is exactly half the tenor plus half a payment period, because principal is repaid in arrears (at the end of the period). So for a 30-year 0% loan, paying monthly, the WAL is 15 + 1 / 24 ≈ 15.04 \{\\displaystyle 15+1/24\\approx 15.04\} years. ## Total Interest WAL allows one to easily compute the total interest payments, given by: WAL × r × P , \{\\displaystyle \{\\text\{WAL\}\}\\times r\\times P,\} where r is the annual interest rate and P is the initial principal. This can be understood intuitively as: "The average dollar of principal is outstanding for the WAL, hence the interest on the average dollar is WAL × r \{\\displaystyle \{\\text\{WAL\}\}\\times r\} , and now one multiplies by the principal to get total interest payments." ## Proof More rigorously, one can derive the result as follows. To ease exposition, assume that payments are monthly, so periodic interest rate is annual interest rate divided by 12, and time t i = i / 12 \{\\displaystyle t\_\{i\}=i/12\} (time in years is period number in months, over 12). Then: WAL = ∑ i = 1 n P i P t i WAL × P ## Computing WAL from amortized payment The above can be reversed: given the terms (principal, tenor, rate) and amortized payment A, one can compute the WAL without knowing the amortization schedule. The total payments are A n \{\\displaystyle An\} and the total interest payments are A n − P \{\\displaystyle An-P\} , so the WAL is: WAL = A n − P P r \{\\displaystyle \{\\text\{WAL\}\}=\{\\frac \{An-P\}\{Pr\}\}\} Similarly, the total interest as percentage of principal is given by WAL × r \{\\displaystyle \{\\text\{WAL\}\}\\times r\} : WAL × r = A n − P ## See also Amortization calculator Amortization schedule Amortizing loan ## Notes and references Fabozzi, Frank J. (2000), The handbook of fixed income securities, ISBN 0-87094-985-3 ## Sources - Weighted-average life · Wikipedia: https://en.wikipedia.org/?curid=15646748 Source: Wikipedia contributors — https://en.wikipedia.org/?curid=15646748&oldid=1348643357 Licence: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation notice: Reformatted for XPay; the source may be abridged, restructured or translated. Consult the cited revision for the original.