Suppose that the yield to maturity of zero-coupon treasury bond from today up to year 1, year 2, and year 3 is 3%, 4%, and 5%, respectively.

a) What are the zero-spot rates from today up to year 1, year2, and year 3, respectively?

b) If the expectations hypothesis holds, what are the expected future 1-year interest rates for the next two years, i.e., E[r1,2] and E[r2,3]? What is the expected future annualized interest rate from year 1 to year 3, i.e., E[r1,3]?