$12.$ An $8\mathrm{.}000\%$ semi$-$annual coupon corporate bond that matures on $3/15/25,$ is purchased for settlement on $4/15/21.$ The yield to maturity is $6\mathrm{.}333\%$ quoted on a street convention semiannual bond basis $($APR$2).$ Accrued interest is calculated using the $30/360$ day count convention.

$($a$)$ What is the flat $($clean$)$ price of the bond on the SDT$?($use the BA II Plus BOND spreadsheet$)$

$($b$)$ What is the accrued interest on the SDT$?($use the BA II Plus BOND spreadsheet$)$

$($c$)$ How many days are there $($T$)$ in the current coupon period?

$($d$)$ How many days are there $($t$)$ between the last coupon date and the SDT$?$

$($e$)$ What is the bond$$s Macauley Duration on the SDT$?($use the alternative formula given on slide #$50$ of chapter $5$ slides and show your work$).$ Remember to use at least $3$ decimal places.

$($f$)$ What is the modified duration of the bond, to at least $3$ decimal places?

$13.$ For the bond in problem $12$ above, if the yield to maturity rises by $65$ basis points $($bps$),$ use the modified duration to calculate the new full bond price. Remember to use at least $3$ decimal places.

$14.$ For the bond in problem $12$ above, if the yield to maturity falls by $80$ basis points $($bps$),$ use the modified duration to calculate the new full bond price. Remember to use at least $3$ decimal places.

$15.$ A $20-$year, $6\mathrm{.}500\%$ annual payment bond settles on a coupon date. The bond's yield to maturity is $9\mathrm{.}400\%.$ What is the bond$$s approximate modified duration to $3$ decimal places? Use yield changes of $+/-25$ bps around the yield to maturity for your calculations.

$16.$ Consider the bond from problem $(15)$ above.

$($a$)$ Calculate the approximate convexity for the bond to at least $3$ decimal places.

$($b$)$ Calculate the change in the full bond price for a $35$ bps change in yield to at least $3$ decimal places including the convexity correction you calculated in part $($a$)$ above.