The following pattern for one$-$year Treasury bills is expected over the next four years:

Year $1$: $4\mathrm{.}5\%$

Year $2$: $4\mathrm{.}0\%$

Year $3$: $3\mathrm{.}5\%$

Year $4$: $3\mathrm{.}0\%$

a$.$ What return would be necessary to induce an investor to buy a

i$.$ two$-$year security

ii$.$ three$-$year security

iii. four$-$year security

b$.$ What is the shape of the yield curve?