2.7 and 2.8

2.7 Suppose that you have $1,000 to invest in the bond market on January 1, 2018. You could buy a one-year bond with an interest rate of 4%, a two- year bond with an interest rate of 5%, a three-year bond with an interest rate of 5.5%, or a four-year bond with an interest rate of 6%. You expect in- terest rates on onc-year bonds in the future to be 6.5% on January 1, 2019,7% on January 1, 2020, and 9% on January 1, 2021. You want to hold your investment until January 1, 2022. Which of the following investment alternatives gives you the highest return by 2022: (a) Buy a four-year bond on January 1, 2018; (b) buy a three-year bond January 1, 2018, and a one-year bond Janu- ary 1, 2021; (c) buy a two-year bond January 1, 2018, a one-year bond January 1, 2020, and an- other one-year bond January 1, 2021; or (d) buy a one-year bond January 1, 2018, and then ad- ditional one-year bonds on the first days of 2019, 2020, and 2021? Suppose that the interest rate on a one-year Trea- sury bill is currently 1% and that investors expect that the interest rates on one-year Treasury bills over the next three years will be 2%, 3%, and 2%. Use the expectations theory to calculate the cur- rent interest rates on two-year, three-year, and four-year Treasury notes. 2.8