spot rate question ( mock 3 morning session q97) note, equivalent, expressed, question

OmarAdnan

question :
treasury spot rates expressed as annual bond equivalent yields:
MATURITY SPOT RATE
6 month – 3.0%
1 YEAR  3.5
1.5 YEAR –4.0
2 YEAR 4.5
two notes :
note 1 : face $1000, 4% semiannual coupon rate, price $991
note 2 : face 1000, 5% seniannual couple price $1008
answer note 1 correctly priced , notes 2 under priced
i think i am wrong in caculate market rate .. who can help me : i use 1.03*1.035*1.04*1.045 get anaul interest rate . not right ?

spartanag07

you have to discount each cash flow at the spot rates given.
note 2 price = [25/1.015] + [25/1.0175^20] + [25/1.02^3] + [1025/1.0225^4] = 1010.05
there fore note 2 underpriced