The discount yield – the term used by the US Treasury (USDT) for bank discount yield (BDY) – is the yield quoted on US T-bills on a simple interest basis (i.e., without compounding) on an actual/360 basis, expressed as a percentage of the instrument’s face value. To calculate the discount yield for T-bills, the following equation is used, where F is face value, P is the purchase price and t the time to maturity in days:
Discount Yield = [(F – P)/F] x (360/t)
To compare the discount yield on T-bills to an investment yield on T-notes and T-bonds, the T-bill discount rate is converted to a seminannual-coupon paying equivalent. The formula used for the conversion of the discount yield of a T-bill to a bond equivalent yield (BEY) is, where DR is the discount rate (discount yield) expressed as a decimal, and t the number of days to maturity:
BEYT-Bill = (365 x DR)/[360 − (t x DR)]