Table $1$: Details of Texas Financials Services Ltd Bond Maturity $15$ July $2029$

Annual Coupon $6\mathrm{.}5\%$

Coupon Payment Frequency Annual

Interest Payment Dates $15$ June and $15$ December

Maturity Date $15$ December $2029$

Day Count Convention $30/360$

Annual Yield$-$to$-$maturity $9\mathrm{.}5\%$

$($a$)$ Calculate the intrinsic value of the bond to be settled on $31$st July $2023$ closest

to and explain why the bond price is different from its nominal value?