When a bill is cashed before its due date, the banker deducts simple interest on the full face value. That deduction is the banker's discount (BD); it is slightly more than the true discount.
1Formulas
BD = SI on the face value A for the unexpired time = ART/100
Banker's gain BG = BD − TD = SI on TD = TD²/PW
Sum due A = (BD × TD)/(BD − TD)
TD = √(PW × BG)