Define and Explain the following concepts:

a$)$ Pure expectation theory of the term structure

b$)$ Liquidity preference theory of the term structure

c$)$ Upward sloping versus Downward sloping yield curves

d$)$ Forward rate vs Spot rate

e$)$ If the $5-$year spot rate is $6\%$ and $3-$year spot rate is $4\mathrm{.}5\%,$ what is the $2-$year $($annualized$)$

forward rate $3$ years from today? $($use the idea developed in class$)$