Suppose you are given the yield curve as follows:

i₁ = 2%; i₂ = 3%; i₃ = 4%; i₄ = 5%. i₅ = 7%, i₁₀ = 10%. These represent the 1-year, 2-year, 3-year and 4-year, 5-year, 10-year bond yields today. Under the pure expectations theory, find a) the expected future one-year rates that will prevail from year 1 to year 2 b) from year 2 to year 3; & c) from year 3 to year 4.