Problem 3. (16 points) Suppose it is 2021 and the 1-year interest rate is 2 percent. The expected 1-year rates in the following four years (2022 to 2025) are 2 percent, 2 percent, 3 percent, and 4 percent.

a. Assume the expectations theory of the term structure, with no term premiums. Compute the interest rates in 2021 on bonds with maturities of 1, 2, 3, 4, and 5 years. Draw a yield curve.

b. Now assume that the term premium for an n-year bond, , is (n)%. (For example, the premium for a 4-year bond is 4%). Compute the interest rates in 2021 on bonds with maturities of 1, 2, 3, 4, and 5 years. Draw a yield curve.