Question

5. A bond has three years to maturity. It pays a 10% coupon rate annually, a $1000 face value, and the market rate of interest is 8%. What is the duration of the bond?

Answer 1

Face value	1000
Ytm =	8%
Time (n) =	3
Coupon amount = (1000*10%) =	100
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
(100*(1-(1/(1+8%)^3))/8%) + (1000/(1+8%)^3)
1051.54194
Bond duration formula = ((Coupon * Time)/(1+i)^1 + (Coupon * time)/(1+i)^2 + ((Coupon +maturity value)* time)/(1+i)^3 )/Bond price
(((100*1)/(1+8%)^1) + ((100*2)/(1+8%)^2) +( ((100+1000)*3)/(1+8%)^3 ))/1051.54194
2.742360188
So, bond duration is 2.74 years