The weights come from present values
Divide each discounted payment by the total bond price to obtain its weight. Multiply each weight by the payment time in years, then add the weighted times. With positive cash flows, those weights sum to one.
| Payment time | Present-value weight | Weighted time |
|---|---|---|
| Year 5 | 1 | 5 years |
Coupons bring some value forward
A regular coupon bond pays some cash before maturity, so its Macaulay duration is normally shorter than its maturity. The size and timing of the coupons determine how much present value arrives earlier. A zero-coupon bond provides the clean boundary case in which duration equals maturity.
Distinguish timing from price sensitivity
Macaulay duration is a timing summary. Modified duration translates it into the coefficient for a small compatible yield change. Keeping the two names separate helps prevent using a year-weighted average without the necessary yield adjustment.