Question

The duration of a par value bond with a coupon rate of 6% (paid annually) and a remaining time to maturity of 5 years is

Answer 1

Bond is par value bond. It means it trade at par value of $1000. Market price if Bond = 1000

If Bond trade at par value then coupon rate and YTM are same.

So YTM (I)= 6%

Number of years to Maturity (n)= 5

Coupon amount= face value*coupon Rate

=1000*6% = 60

Bond duration formula = ((Coupon * Time)/(1+i)^1 + (Coupon * time)/(1+i)^2 + (Coupon * time)/(1+i)^3 + (Coupon * time)/(1+i)^4 +(Coupon * time)/(1+i)^5 +(maturity amount * time)/(1+i)^5)/ Bond price   

=((60*1)/(1+6%)^1 + (60*2)/(1+6%)^2 + (60*3)/(1+6%)^3 +(60*4)/(1+6%)^4 +(60*5)/(1+6%)^5 + (1000*5)/(1+6%)^5)/1000

=4.465105613

So Duration of bond is 4.4651 Years