How are the purchase price and the investment rate (APR) related?
If you consider the purchase price as the “principal” of the investment and the difference between face value and purchase price the “interest,” if you calculate (interest/principal)*(365/days of bill) you get the APR. The Treasury does this calculation for us to 1/1000 basis point, however the price is actually more accurate to 1/1000 of a cent for a $1000 bill.