What does the term Discount Rate mean when it comes to Treasury Bonds?

External question — Personal Finance Stack Exchange Author: Bob Original post: https://money.stackexchange.com/questions/163999 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Recently bought a Treasury bond. The bond comes due at par (100) on 1/14/2025. The settlement day for the trade is 9/17/2024. I paid 98.450025 for the bond. On the trade confirmation it said: YIELD INFORMATION: DISCOUNT RATE 4.689%. BOND EQUIVALENT YIELD 4.828%. Using an online date calculator, I find the bond comes due in 120 days. However, it would have been 119 days if did not count the end points. I calculated the bond equivalent yield as follows: (1+(100-98.450025)/98.450025 ) ^(365/120) - 1 This gives me a bond equivalent yield as: 4.866% That number does not match the trade confirmation exactly but I figure it is close enough. If somebody could come up with a different way to calculate the bond equivalent yield and match the trade confirmation I would like to know. My real question is, how do I calculate the discount rate for the bond?

External answer — Personal Finance Stack Exchange Author: D Stanley Original post: https://money.stackexchange.com/a/164005 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. The discount rate is simply the discount (par minus price) you received divided by the par amount, then annualized: (100 - 98.45) / 100 * (360/119) = 4.689% The bond equivalent yield is calculated as the return on investment, then annualized similarly: ((100 / 98.45) - 1) * (365/119) = 4.829% They both measure the same thing from different perspectives - how much below the value you pay (discount) versus what percentage return you get (yield). Bond Equivalent Yield is more effective for comparing against other interest-bearing investments. If you're wondering why your formula yields a different number, It assumes that your investment compounds every 120 days, which is true if you take the face value in 120 days and buy another bond at the same yield (if you can).