$On$ May $31st2021,$ the yield $on$ a one$-$year $US$ Treasury bill was $0\mathrm{.}05\%.$ According $to$ the New York Fed$s$

Survey $of$ Consumer Expectations, the one$-$year rate $of$ inflation for the year starting May $31st2021is$ estimated $tobe4\%.$ Suppose you also believe that the one$-$year interest rate $on$ May $31st2022$ will $be2\%.$ Furthermore, you believe this rate will continue $to$ rise $to2\mathrm{.}5\%on$ May $31st2023,$ and $3\%on$ May $31st2024.$

$a.$ Based $on$ this information, what $is$ the expected real rate $of$ return $on$ a one$-$year $US$ Treasury bill?

$b.If$ you are certain about these estimates $of$ future interest rates, what current term structure $of$ interest rates $(thatis$

yields $onUS$ Treasury bills maturing $in$ two, three, and four years$)is$ consistent with these expectations?

$c.$ Plot the yield curve.

$d.$ Suggest $at$ least one theory $to$ justify why you believe the one$-$year interest rate will start $to$ rise a year from now.