$3a.$ Suppose the current one$-$year rate $(one-$year spot rate$)$ and expected one$-$year $T-$bill rates over the

following three year $(i.e.$ years $2,3,$ and $4,$ respectively$)$ are $as$ follows:

${?}_0{R}_1=6\%$

$E{(}_1{R}_1)=7\%$

$E{(}_2{R}_1)=7\mathrm{.}5\%$

$E{(}_3{R}_1)=7\mathrm{.}85\%$

Using the unbiased expectations theory, calculate the current $(long-$term$)$ rates for one$-,$ two$-,$ three$-,$

and four$-$year maturity Treasury $securities.$ Plot the resulting yield curve.

$3b.$ Suppose the current one$-$year rate $(one-$year spot rate$)$ and expected one$-$year $T-$bill rates over the

following three year $(i.e.$ years $2,3,$ and $4,$ respectively$)$ are $as$ follows:

${?}_0{R}_1=2\mathrm{.}35\%$

$E{(}_1{R}_1)=2\mathrm{.}87\%$

$E{(}_2{R}_1)=3\mathrm{.}05\%$

$E{(}_3{R}_1)=3\mathrm{.}15\%$

Using the unbiased expectations theory, calculate the current $(long-$term$)$ rates for one$-,$ two$-,$ three$-,$

and four$-$year maturity Treasury $securities.$ Plot the resulting yield curve.