The weighted average life of a bond is the time it takes for the loan issuer to repay all of the principal back to the investor, and each repayment time is weighted by the repayment amount. The weighted average life of most bonds is simply its time until maturity. For amortizing bonds, which repay parts of the principal along with coupon payments over the course of the lifetime of the bond, weighted average life requires a little bit of calculation.
Multiply each principal repayment by the number of each payment period. For example, if you have a bond with an outstanding principal of $100, and $10 was repaid in the first year, $20 was repaid in the second year, $30 was repaid in the third year and the remaining $40 was repaid in the fourth year, then multiplying each payment period's number by its repayment amount gives $10 ($10 x 1), $40 ($20 x 2), $90 ($30 x 3) and $160 ($40 x 4). These are the weighted payments.
Add up the weighted payments. Using the same example, adding up $10, $40, $90 and $160 gives $300. This is the weighted total of principal repayments.
Divide the weighted total of principal repayments by the outstanding principal, or face value of the bond. So, if the bond's face value is $100, and the weighted total of principal repayments is $300, dividing $300 by $100 gives 3. The weighted average life of the amortizing bond is thus three years.