You observe the yields of the following Treasury securities (all yields are shown on a bond-equivalent basis):

Year (Period)	Yield to Maturity (%)	Spot Rate (%)
0.5 (1)	10.00	10.00
1.0 (2)	9.75	9.75
1.5 (3)	9.50	9.48
2.0 (4)	9.25	9.22
2.5 (5)	9.00	8.95
3.0 (6)	8.75	?
3.5 (7)	8.50	?
4.0 (8)	8.25	8.14
4.5 (9)	8.00	7.86
5.0 (10)	7.75	7.58

All the securities maturing from 1.5 years on are selling at par(=$100). The 0.5 and 1.0-year securities are zero-coupon instruments. Answer the below questions.

(a) (10 pts) Calculate the missing spot rates.

(b) (5 pts) What should the price of an 5% 4-year Treasury security (with a maturity value of $1,000) be?

(c) (5 pts) If the market priced the 5% 4-year Treasury bond in part (b) based on the YTM of 4-year security indicated in the table above, find an arbitrage strategy and identify arbitrage profits.