One day people found that U.S. Treasury securities with the following maturities and coupon rates trading at the prices shown below (per $100 face value):

a. What is the zero-coupon yield curve for maturities of 1 to 3 years?(Three answers with percentage) YTM: yield to maturity.

b. The U.S. Treasury has just issued a risk-free three-year bond, paying annual interest and with a face value of $100. The bond was issued at a 10% premium. What was the coupon rate of this bond?

c. Suppose the term structure is flat at 1.5% (effective annual rate or EAR) for maturities of 4 years and longer horizons, but that the yield curve for maturities of 1 to 3 years is still the same as in part (a). The US Treasury Department is considering taking advantage of the low interest rate environment by issuing some perpetual debt (i.e. a bond that promises a fixed coupon forever). If the bond makes annual coupon payments and is to be issued at its par value of $100, what must the coupon rate be?

Please show detailed calculation!

Maturity 1 year 2 years 3 years Coupon Rate 0% 0% 0% Current Price 99.50 98.52 97.36 Maturity 1 year 2 years 3 years Coupon Rate 0% 0% 0% Current Price 99.50 98.52 97.36