For the below question, could someone please help me on the doubt I have: Given the following spot and forward rates what is the closest value of a 4 year 10% annual pay $1000 par value bond: Current 1 year spot rate is 5.5% 1y1y is 7.63% 2y1y is 12.18% 3y1y is 15.5% A. $996 B. $1009 C.$1086 I got this wrong because I calculated the spot rate as (1+r)^4 = 1.055*1.0763*1.1218*1.1550 Which gave me spot rate as 10.13% and the PV as 996 Answer is 100/(1.055) + 100/(1.055) (1.0763) + 100/(1.055) (1.0763) (1.1218) + 1100/(1.055) (1.0763) (1.1218) (1.155) = 1009. Doubt = why this cannot be solved as I did?
By doing this, you are assuming that this spot rate, S4 applies to each year i.e. S1=S2=S3=S4
Rather, S1= 5.5%; S2= 6.56%; S3=8.40% and S4=10.13% and you discount each period coupon with the respective spot rate.
Is this question from schweser? The forward rate denotation seems to be XyZy where X is the no of periods from today and Z is the length of the forward rate.