We observe the following annualized yields on four Treasury securities:

Maturity (Years)	Yield-to-maturity (%)
0.5	4%
1	4.5%
1.5	5%
2	5.5%

The par is $1000 for all the securities. The one with 0.5- year to maturity is a zero coupon bond. All other securities are coupon-bearing bonds selling at par. Note that, for par bonds, the coupon rate equals YTM. 1. Calculate the sport rates for the maturities of 0.5, 1, 1.5, and 2 years 2. What is the price of a 2-year bond with an 8% annual coupon rate (assume $1000 par)? 3. Suppose a 1-year zero-coupon bond with a par value of $1000 is selling at $900. Is there any arbitrage opportunity? If there is, construct an arbitrage portfolio and show the profit. 4. Calculate the one-period-ahead forward rates from 0 to 0.5, from 0.5 to 1, from 1 to 1.5, and from 1.5 to 2. 5. One year from now, you plan to purchase a then one-year bond with a 1000 par and an 8% annaul coupon rate. Waht is the expected price of the bond? Assume the expectation hypothesis holds. Under the expectation hypothesis, the expected future spot rate equals the forward rate. *** Show All Work ***