Monetary Authority of Singapore $($MAS$)$ issued a $180$ day Tresury $($T$-$bill$)$ with face value of $$100$ on $15$ December $2022,$ which is currently traded at $$98\mathrm{.}5$ in the market on $15$ march $2023.$ Assume the yeild remains unchanged thought out the maturity $($YTM is flat$),$ and $365$ days a year.

Required:

$($a$)$ Compute the Yield to Maturity $($YTM$)$ and the price of T$-$Bill on the issue date. Assume YTM is flat.

$($b$)$ if the interest rate is expected to decrease, does $60$ day T$-$bill perform better or worse than $180$ day T$-$ bill assuming other things being constant? Discuss.