Given the information of a “pure” yield curve below: Maturity (years) 1 2 3 4 Yield to Maturity (%) 3% 4% 5% 6% a

a) Assuming face value to be $100

Annual coupon =$100*10% =$10

Present value of bond = 10/1.03+ 10/1.04^2+10/1.05^3+10/1.06^4+100/1.06^4 = $114.72

So, the bond's present value is 114.72% of the face value

b) YTM (r) of the bond is given by

10/(1+r)+ 10/(1+r)^2+10/(1+r)^3+10/(1+r)^4+100/(1+r)^4 = $114.72

=> 10/r*(1-1/(1+r)^4)+100/(1+r)^4 = $114.72

Solving , r = 0.05773 or 5.77%

c) Short rate in year 1 = spot rate =3%

Short rate in year 2 = 1.04^2/1.03 -1 = 0.050097 or 5.0097%

Short rate in year 3 = 1.05^3/1.04^2 -1 = 0.070289 or 7.0289%

Short rate in year 4 = 1.06^4/1.05^3 -1 = 0.090575 or 9.0575%