there are two bonds on the market:

(a)One-year $100 zero selling for $95.2381

(b)Two-year 8% coupon $1000 par bond selling for $1000

(1) Assume that the pure expectations theory for the term structure of interest rates holds and no liquidity premium exists. Find implied 1 year rate 1 year from now? show formulas

(2) for the same bonds, assume a liquidity premium of 0.5% for the 2-year long rate (i2t), what is the implied 1-year rate 1 years from now?

(3) your company plans to issue two-year coupon bonds but the current one-year rate suddenly increase to 10% and the two-year long rate becomes 9%, what coupon rate that you need to sell at par?