By Linear Interpolation I am not getting a close solution, i.e. First, I calculated the discount rates for the T-Bill and T-note, (0.962, 0.9284 respectively, therefore I have obtained the Spot Rates (3,95%; 7.71%, respectively) I have 2 years, i.e T1=1 T2=2 and T= 18 Months (1.8y) The Linear interpolation formula : {(T2-T) x R(0.1) + (T-T1) R(0,2) } / (T2-T1), thus: (2-1,8) x 3,95%+ (0,8 x 7,71%) equals to 6,958%.
I get 3.9118% BEY for the T-Bill and 3.7904% BEY for the T-Note. Your calculation of the 2-year spot rate is way off.
I’m not sure if by 18-month discount rate they mean the spot rate or the par rate. I would think that they mean the par rate as computing the spot rates will be very difficult, given that you don’t have prices for 6-month and 18-month bonds.
Finally, 18 months is 1.5 years, not 1.8 years, so the weights on your interpolation are incorrect; they should be 0.5 and 0.5.
You are correct, 1,5 equals 18 months (I have made a tragic mistake), therefore the solution is d: 5,83 %. Try plugging it and you will get the correct answer. Remember we need to get R(0,15), using linear interpolation, If I understood well the model, which it is not very often used in practice. I think that you have made a mistake regarding the 2y spot rate.We can solve it as:
We know already that the first bond is a zero coupon bond i.e his discount factor equals to 0.962. Now, let’s work on the second one. 100,4= 4 (coupon rate) x B(0,1) + 104 (Face value plus the final coupon) x B(0,2) We plug the value of B(0,1) therefore B(0,2) is solved as a linear equation, whereas the value of B(0,2) is then used to get the value of R(0,2).