$2.$ The competitive auction results for Treasury securities in February $2024$ up through $5-$year notes are listed in the associated Excel file. Assume the $2-,3-,$ and $5-$year notes pay their coupons every six months.

a$.$ Calculate the continuously compounded zero rates for each of these bonds.

Assume that any payment made that does not align with one of the terms above has the same zero rate as the next maturing bond $($e$.$g$.$ the coupon payment that will occur in $18$ months on each of the notes will use the two$-$year zero rate$).$

b$.$ Calculate the forward rates between each of these times.

c$.$ A ten$-$year note issued in February $2019$ had coupon rate of $2\mathrm{.}625\%$ and was priced at auction to be $99\mathrm{.}442089.$ Use the zero rates you calculated in part a to estimate its price in February $2024.$

d$.$ Given the price you calculated in part c$,$ what is this ten$-$year bond's continually compounded yield to maturity?

Coupon Rate Price $($per $$100$ par value$)$

$4-$week $99\mathrm{.}589333$

$8-$week $99\mathrm{.}180222$

$13-$week $98\mathrm{.}677972$

$17-$week $98\mathrm{.}276153$

$26-$week $97\mathrm{.}421667$

$52-$week $95\mathrm{.}252833$

$2-$year $4\mathrm{.}625\%99\mathrm{.}875391$

$3-$year $4\mathrm{.}125\%99\mathrm{.}877119$

$5-$year $4\mathrm{.}250\%99\mathrm{.}688225$