Derive the formula for the Macaulay duration of a coupon bond with inexact number of periods to maturity:

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QUESTION 1. Derive the formula for the Macaulay duration of a coupon bond with inexact number of periods to maturity: D D where n Number of remaining coupons, Dn Duration computed at previous coupon date k Coupon frequency dIN Number of days from settlement to next coupon date, d PN Number of days from previous coupon date to next coupon date. Use the following steps: a. Let Pn be the price of the bond computed at the previous coupon date and show that l-w where P is the current bond pice and F. is the bond pice at previous copuon date. b. By differentiating the above equation with respect to r, show that l-w OP 1- or c. Substitute this into the equation for the duration 1+ QUESTION 1. Derive the formula for the Macaulay duration of a coupon bond with inexact number of periods to maturity: D D where n Number of remaining coupons, Dn Duration computed at previous coupon date k Coupon frequency dIN Number of days from settlement to next coupon date, d PN Number of days from previous coupon date to next coupon date. Use the following steps: a. Let Pn be the price of the bond computed at the previous coupon date and show that l-w where P is the current bond pice and F. is the bond pice at previous copuon date. b. By differentiating the above equation with respect to r, show that l-w OP 1- or c. Substitute this into the equation for the duration 1+