What is Discount Rate of US Treasury Bill?

Discount Rate of US Treasury Bill (T-Bill) is the annualized rate of the discount you get off the face value when you purchase the T-Bill.

The following formula defines the Discount Rate in a very easy-to-understand form:

$d={\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}\times {\displaystyle \frac{(F-P)}{F}}$
$P=\text{Purchase price}$
$F=\text{Face value}$
$d=\text{Discount Rate}$
$\mathrm{Days}=\text{Number of days to maturity}$
$\mathrm{Year}=360=\text{Constant number of days in a year}$

Different parts of the formula can be easily remembered as:

$\text{Price discount}:F-P$
$\text{Simple discount percentage in decimal form}:{\displaystyle \frac{(F-P)}{F}}$
$\text{Annualization factor}:{\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}$

Of course, we can transform the about formula into different forms to calculate discount rate, purchase price and face value:

$d={\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}\times (1-{\displaystyle \frac{P}{F}})$
$P=F\times (1-d\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})$
$F={\displaystyle \frac{P}{(1-d\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})}}$

Based above equations, you have two ways to get higher discount rate when purchasing T-Bills:

• Lower the purchase price to get higher discount rate.
• Purchase shorter T-Bills for the same price to get higher discount rate.

Here is an example of 26-week T-Bill bought through TreasuryDirect.gov with a discount rate of 4.170% reported as "Yield":

CUSIP: 912797NW3
Type: 26-Week Bill 
Par Amount: $10,000.00 (Face value) 
Purchase Price: $9,789.18

Yield: 4.170% (Discount rate)
Price per $100: 97.891833

Discount: $210.82
 
Issue Date: 2024-12-26
Maturity Date: 2025-06-26

We can use this example to verify the discount rate formula:

$d={\displaystyle \frac{\mathrm{Year}}{\mathrm{Days}}}\times (1-{\displaystyle \frac{P}{F}})={\displaystyle \frac{360}{182}}\times (1-{\displaystyle \frac{9789.18}{10000}})=0.041700006593406=\text{4.170\%}$
$P=F\times (1-d\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})=10000\times (1-0.0417\times {\displaystyle \frac{182}{360}})=9789.1833333333=\text{\$9,789.18}$
$F={\displaystyle \frac{P}{(1-d\times {\displaystyle \frac{\mathrm{Days}}{\mathrm{Year}}})}}={\displaystyle \frac{9789.18}{(1-\mathrm{0.0417}\times {\displaystyle \frac{182}{\mathrm{360}}})}}=9999.9965948811=\text{\$10,000.00}$

We have also provided a discount rate online calculator for you to use. Click this link "T-Bill 912797NW3 settled on 2024-12-26 with a price of 97.891833", you will see the discount rate of 4.1700% displayed.

Note that the number of days in a year is considered as 360 in the discount rate formula. But it is considered as 365 or 366 in other US Treasury formulas.

Related topics:

Discount Rate to Price Converter for T-Bills

Price to Discount Rate Converter for T-Bills

⇒ High/Median/Low Rate of US Treasury Bill

⇐ Price Discount/Premium of US Treasury Bill

⇑ Performance Measurements of US Treasury Bills

⇑⇑ US Treasury Securities