# The interest rate of a (U.S. Treasury) "Floating Rate Note" (FRN)

I am having trouble to reproduce the calculation of the interest rate of a (U.S. Treasury) "Floating Rate Note" (FRN). Can you help me to find my error?

The calculation is described here: https://www.treasurydirect.gov/marketable-securities/floating-rate-notes/#calculating .

Let's use the example of 2-Year FRN CUSIP 91282CFS5, issued 10/31/2022, with spread of 0.140%.

From the link above, we know "This rate is tied to the highest accepted discount rate of the most recent 13-week Treasury bill".

The most recent 13-week auction was 01/09/2023, resulting in a price of \$98.847333 per \$100. Looking at https://treasurydirect.gov/auctions/announcements-data-results/ , we read that it is CUSIP 912796YU7, with

Issue Date High Rate Investment Rate
01/12/2023 4.560% 4.677%

Returning to our FRN, we see that for the accrual period January 10th-11th, there are new rates, seemingly in response to the new 13-week auction:

Daily Index (%) Daily Interest Accrual Rate (%) Daily Accrued Interest per \$100
4.613174525 4.753174525 \$0.013203263

Clearly the 4.75% is found by adding the spread of 0.14% to the 4.61%, so that is fine. But I am unclear on where the "highest accepted discount rate" is coming from. Is it the 4.61317...%?

It is neither the "High Rate" nor the "Investment Rate" of the 13-week; it lies between them.

How do I calculate this value of 4.613174525, from information about the 13-week T-bill?

It seems the behavior of a T-bill is fully determined by the price per \$100, in this case \$98.847333.

Note: I have read this answer, where it says "(the) highest accepted bid was for the high rate", but I am still missing something, for I need the "highest accepted discount rate".