Do the following problem @ $28$ points. Show all work for full credit.

Given the following data on debt U$.$S$.$ Treasury debt instruments:

$1-$year note yield $=4\mathrm{.}42\%-0=4\mathrm{.}42,7-$year note yield $=5\mathrm{.}64\%-1\mathrm{.}12=4\mathrm{.}52$

$2-$year note yield $=4\mathrm{.}69\%-17=4\mathrm{.}52,8-$year note yield $=5\mathrm{.}70\%,1\mathrm{.}22$~~$4\mathrm{.}48$

$3-$year note yield $=5\mathrm{.}02\%41=4\mathrm{.}61,9-$year note yield $=5\mathrm{.}86\%,1\mathrm{.}30=4\mathrm{.}56$

$4-$year note yield $=5\mathrm{.}02\%,.\mathrm{.}63=4\mathrm{.}39,10-$year note yield $=5\mathrm{.}95\%,1\mathrm{.}372,4\mathrm{.}58$

$,5-$year note yield $=5\mathrm{.}35\%-\mathrm{.}82=4\mathrm{.}5311-$year note yield $=5\mathrm{.}90\%,1\mathrm{.}42=4\mathrm{.}48$

$,6-$year note yield $=5\mathrm{.}50\%-\mathrm{.}98=5\mathrm{.}3912-$year note yield $=5\mathrm{.}99\%,-1\mathrm{.}45-4\mathrm{.}54$

And constant premiums of $0,\mathrm{.}17\%,\mathrm{.}41\%,\mathrm{.}63\%,\mathrm{.}82\%,\mathrm{.}98\%,1\mathrm{.}12\%,1\mathrm{.}22\%,1\mathrm{.}30\%,1\mathrm{.}37\%,1\mathrm{.}42\%,1\mathrm{.}45\%,1\mathrm{.}47\%$

a$.$ Calculate the expected market yields for a $(1,5,2)$ path.

b$.$ Calculate the expectations yields for a $(3,4,1)$ path.

c$.$ Calculate the real world yield for a $(3,5)$ path.

d$.$ Calculate the expected preferred habitat yield for a $5-$year note purchased at the beginning of year $2.$

e$.$ Calculate the expectations yield on a $4-$year note purchased at the beginning of year $5.$

f$.$ Determine the expectations yield on a $10-$year note purchased today.

g$.$ Determine the yield on a $12-$year Treasury note purchased today.

h$.$ Describe the yield curve and provide a general interpretation of what implies about the economy.