The 4-week T-Bill auctioned today, May25, at 99.552778 for a May 30 settlement. Treas Direct reports the 'Investment Yield " as 5.872%. But that number asssumes the achieved interest amount is reinvested when it is received and that the whole amount is carried forward for a full year at the same original interest rate. That is a slightly unrealistic assumption, because the rates on the 4-week vary weekly.
But a gain of (roughly) $4.47 for a 28-day holding period on a purchase price of (roughly) $995.53 is a gain of (roughly) 1.6044 bps/day, or a simple interest rate of (roughly) 5.86% annually, which is close enough to Treasury Direct’s projection for me to accept their projection for the sake of convenience.