You observe the yields of the following Treasury securities (all yields are on a bond-equivalent basis) as shown in Table 1. All the securities maturing from 1.5 years on are selling at par. The 0.5 and 1.0-year securities are zero-coupon instruments. Answer the below questions.

Table 1
Year (Period)	Yield to Maturity (%)	Spot Rate (%)
0.5 (1)	5.25	5.25
1.0 (2)	5.50	5.50
1.5 (3)	5.75	5.76
2.0 (4)	6.00	6.02
2.5 (5)	6.35	???
3.0 (6)	6.65	???
3.5 (7)	6.95	???
4.0 (8)	7.15	???
4.5 (9)	7.50	???
5.0 (10)	7.85	???

a. Calculate the missing spot rates. (8 points)

b. What is the six-month forward rate starting in the fourth year? (2 points)

c. Based on the theoretical spot rate curve estimated, what should the price of a 5.25% (paid semiannually) 5-year Treasury security with par value $1,000,000 be? (2 points)