As of June $7,2024,$ Treasury yields were as follows:

$1-$year $5\mathrm{.}17\%$

$2-$year $4\mathrm{.}87\%$

$3-$year $4\mathrm{.}65\%$

$5-$year $4\mathrm{.}46\%$

$10-$year $4\mathrm{.}43\%$

$30-$year $4\mathrm{.}55\%$

Use these yields to answer the questions below.

a$.$ What do the rates above imply about the shape of the yield curve? Explain. $(2$ points$)$

b$.$ Using the pure expectations theory of the term structure of interest rates, carefully explain how the general shape of the yield curve described in $($a$)$ could come about. $(3$ points$)$

c$.$ Use the yields above to estimate the two$-$year forward rate one year from now $($t$+1$r$2).(3$ points$)$

d$.$ Use the yields above to estimate the one$-$year forward rate two years from now $($t$+2$r$1).(3$ points$)$

e$.$ Do your estimates in $($c$)$ and $($d$)$ support your answer in $($a$)?$ Explain. $(2$ points$)$