A tool that measures the average length of time the holder of a bond has to wait before receiving cash interest payments. The duration of a zero-coupon bond is equal to the life of the bond. However, the duration of an interest-bearing bond that lasts “n” years is less than “n” years, because the holder receives coupon payments on a periodical basis before maturity date, not just the principal at the end of the bond life. The duration of a bond can be calculated using the following formula:

where y is the bond yield (continuously compounded), c_i is the cash flows at time t_i, and B is the bond price (i.e., the present value of all coupon payments and the principal):

As such, the duration is a weighted average of the times of payment (e.g., the weight assigned to time t_i is equal to the proportion of the bond’s present value provided by the cash flow at time t_i). The sum of the weight is one.

For an example, see: tutorial- bond duration: an example.