U$.$S$.$ Treasury Bills are quoted based on an Act$/360$ discount yield, $,$ where is the number of days from settlement date to maturity date.

Provide a formula for converting the Act$/360$ discount yield to an Act$/360$ simple $($add$-$on$)$ yield, $.$

The semiannual coupon equivalent yield $($bond equivalent yield, BEY$)$ of a T$-$Bill is defined as follows: let $(366$ if there is a leap day between settlement and maturity dates$).$ If $,$ the BEY solves