Schweser spot rate question note, equivalent, question, selling

mkytz15

book 5: fixed Income. study session16 comprehensive problem 4
The yield to maturity on a bond equivalent basis on 6month and 1year Tbills are 2.8% and 3.2%, respectively. A 1.5 year, 4% Treasury note is selling at par.
A. What is the 18 month Treasury spot rate?
the answers says since the tbills are zero coupon instruments, their YTMs are the 6 month and 1 year spot rates.
100=2/(1+0.028/2)+2/(1+0.032/2)^2+102/(1+S/2)^3
since it is treasury note, we use coupon 2 to calculate. And the answer use 2/(1+0.032/2)^2 which is1 year Tbills yield 3.2% to calcuate. I fell puzzled about this.
Because in P115 spot rate calculation, we need to calculate 2 year spot firstly,which is not equal yield 3.2%. Then calcuate 3year spot rate.
So how can we use tbill’s attribute here? (That is tbills are zero coupon instruments, their YTMs are the 6 month and 1 year spot rates. ) How can we avoid calculate 1 year spot rate, just use yield rate 3.2%?
Thanks,

Spongebob

For any zero coupon bond the YTM = spot rate.
For a coupon bond the YTM does NOT equal spot rate. The YTM for a coupon bond is the discount rate that when applied to all coupon and principal payments makes the NPV = Market price.
Since both the 6mos and 1 year TBills are zero coupon instruments, their YTMs are the spot rates.
The 18 month TNote is not a zero coupon instrument  it makes payments at 6 months, 12 months and 18months.
If you were to calculate the (already known) market price you would discount each of those three payments using the spot price that corresponds to that time.
Since you are given the market price, 2 out of 3 spot rates, and the YTM on the on the TNote, you can solve for the one unknown, the 18 month spot rate, using the formula from the book.
I’m not really sure if this will help because I’m not really sure what the question was. Let me know if you need further clarification.