How "Yield" of US Treasury Bill is calculated on Fidelity Investments quoting system?

If you are using Fidelity Investments brokerage account to buy or sell US Treasury Bills, you will see a list of current bidding (and asking) prices and yields provided by the Fidelity Investments quoting system.

Here is a screenshot of trade order placed on 2025-01-17 to buy a US Treasury Bill:

CUSIP: 912797PE1
Description: UNITED STATES TREAS BILLS ZERO CPN 0.00000% 07/17/2025 
Maturity: 2025-07-17

The term "Yield" on Fidelity system represents BEY (Bond Equivalent Yield) defined as:

$F=P\times (1+i\times {\displaystyle \frac{{\displaystyle \frac{\mathrm{Year}}{2}}}{\mathrm{Year}}})\times (1+i\times {\displaystyle \frac{\mathrm{Days}-{\displaystyle \frac{\mathrm{Year}}{2}}}{\mathrm{Year}}})$
$P=\text{Purchase price}$
$F=\text{Face value}$
$i=\text{BEY (Bond Equivalent Yield)}$
$\mathrm{Days}=\text{Days to maturity}$
$\mathrm{Year}=\text{365 or 366}=\text{Actual number of days in the year}$

Note that if the T-Bill is maturing in less than or equal to one half-year, the compounding interest should be replaced by a simple interest.

To verify "Yields" displayed on the Fidelity system, we can use our T-Bill online calculator to convert yields (BEY - Bond Equivalent Yields) to prices. The results are listed below:

          Buyer's Quotes             |       FYIcenter.com    
Bid Yield    Qty (min)    Bit Price  |  BEY/Yield   Discrepancy   
---------   -----------   ---------  |  ---------   -----------
    4.318     1000(200)   97.948     |     4.3202       -0.0022
    4.324   15000(1000)   97.946     |     4.3245       -0.0005
    4.324    40000( 50)   97.946     |     4.3245       -0.0005
    4.332    25000( 50)   97.942     |     4.3331       -0.0011

          Seller's Quotes            |       FYIcenter.com
Ask Price    Qty (min)    Ask Yield  |  BEY/Yield   Discrepancy
---------   -----------   ---------  |  ---------   -----------
   97.959      351(200)   4.297      |     4.2965        0.0005
   97.961   15000(1000)   4.293      |     4.2922        0.0008
   97.965    25000( 50)   4.284      |     4.2836        0.0004
   97.967    63531( 50)   4.279      |     4.2793       -0.0003

As you can see the discrepancies are bigger than rounding differences except for the last two. So Fidelity is not really using the BEY (Bond Equivalent Yield) formula to calculate the bidding or asking yields.

Since Fidelity is not publishing their "Yield" formula, we don't know how Fidelity is actually calculating "Yields".

⇒ Online Resources on US Treasury Bill

⇐ Buy/Sell US Treasury Bills with Fidelity Investments

⇑ Introduction of US Treasury Bills

⇑⇑ US Treasury Securities