The expected path of one$-$year interest rates over the next five years is $3$ percent, $4$ percent, $6$ percent, $7$ percent, and $5$ percent, respectively. Given that the expectations theory is the correct theory of the term structure:a$)$ Draw the yield curve for the $5-$year period. $(10$ pts$)$b$)$ If the investors prefer shorter$-$term bond to longer$-$term bond, what happen to the shape of the yield curve? $(5$ pts$)$