Suppose that a risk$-$neutral investor has a choice between buying a one$-$year bond paying $5$ percent today, a two$-$year bond paying $5\mathrm{.}4$ percent today, a three$-$year bond paying $5\mathrm{.}8$ percent today, or a four$-$year bond paying $6\mathrm{.}2$ percent today, if a one$-$year bond purchased one year from now is expected to have an interest rate of $6$ percent, a one$-$year bond purchased two years from now is expected to have an interest rate of $7$ percent, and a oneyear bond purchased three years from now is expected to have an interest rate of $8$ percent. Arrange the sequence of bonds giving the interest rate from highest to the lowest. Which bond would the investor buy? Show your work. $($