Question

calculate the duration of a 6% 1,000,000 par bond

Answer 1

Assume par value of the bond is 100. Assumed maturity period is 5years. Assumed bond is trading at par, since bond is trading at per then Yield to maturity (YTM) is equals to coupon rate, i.e.6%

Duration = (1+YTM)/YTM - {(1+YTM)+[years*(Coupon rate-YTM)]}/[Coupon rate*{[(1+YTM)^years]-1}+YTM]

= (1+0.06)/0.06 - {(1+0.06)+[5*(0.06-0.06)]}/[0.06*{[(1+0.06)^5]-1}+0.06]

= (1.06/0.06)-{1.06+(5*0)}/{0.06*[(1.06^5)-1]+0.06}

= 17.6667-{1.06/[0.06*(1.33822558-1)]+0.06}

= 17.6667 - {1.06/[0.06*0.33822558]+0.06}

= 17.6667 - {1.06/(0.02029353+0.06)}

= 17.6667-(1.06/0.08029353)

= 17.6667-13.2016

= 4.4651years or 4.47years