About the Bond Equivalent Yield Calculator
Treasury bills, commercial paper and other money market instruments are sold at a discount and repay face value at maturity. Their quoted “discount rate” understates the return you actually earn, because it divides by face value and uses a 360-day year. The bond equivalent yield (BEY), which the Treasury calls the investment rate, restates that return on the price you pay over a 365-day year so it can be compared with coupon bonds, CDs and savings accounts.
This bond equivalent yield calculator is for investors comparing T-bills with other cash options and for students studying money market yields. Enter the face value, purchase price and days to maturity to get the BEY, the bank discount yield, the money market (CD-equivalent) yield, the effective annual yield and the dollar return.
For terms of up to half a year (182 days) the BEY is a simple annualised return. For longer bills it uses the Treasury’s formula from 31 CFR Part 356, Appendix B, which assumes a semiannual coupon-equivalent so that the result is comparable with a note or bond yield. A 365-day year is used throughout.
With the default inputs, the bond equivalent yield (investment rate) is 5.077%. Change any value above to recalculate instantly.
How to use the bond equivalent yield calculator
- 1Enter the face value of the bill or note.
- 2Enter the price you pay (or the auction price per $100 multiplied up).
- 3Enter the number of days until maturity.
- 4Compare the bond equivalent yield with CD, savings or bond yields.
Formula and method
The bond equivalent yield measures the gain relative to the price paid and annualises it over a 365-day year. For bills with half a year or less to maturity that is a simple-interest calculation. For longer bills, the Treasury assumes the investor would receive a coupon-equivalent payment after half a year and reinvest it, which leads to the quadratic formula above; this is the investment rate published with Treasury bill auction results.
The bank discount yield divides the gain by face value and uses 360 days, so it is always the lowest figure. The money market yield divides by the price but still uses 360 days. The effective annual yield compounds the holding-period return over a full year, (F/P)^(365/d) − 1, comparable with an APY.
- F
- Face value repaid at maturity
- P
- Purchase price
- d
- Days to maturity
Worked examples
13-week T-bill: $10,000 face bought for $9,875
You earn $125 on $9,875 in 91 days: 125 ÷ 9,875 × 365 ÷ 91 = 5.077% BEY. The quoted discount rate is only 4.945% because it divides by face value and uses a 360-day year.
26-week bill at $9,750
A $250 gain on $9,750 over 182 days annualises to 250 ÷ 9,750 × 365 ÷ 182 = 5.142%, still using the simple formula because the term is exactly half a year.
52-week bill at $9,550 (long-term formula)
For 364 days the Treasury quadratic applies: a = 364/730 − 0.25, b = 364/365 and c = −450/9,550, giving a BEY of 4.671%. That is slightly below the simple 4.725% effective yield because it assumes semiannual compounding.
Frequently asked questions
What is bond equivalent yield?+
Bond equivalent yield is the annualised return on a discount security based on the price you pay and a 365-day year. It lets you compare a T-bill or commercial paper with coupon bonds and other investments quoted on a bond basis.
Why is the BEY higher than the T-bill discount rate?+
The discount rate divides the dollar gain by face value instead of the lower price you actually pay, and annualises it using 360 days instead of 365. Both choices make it smaller than the true return.
What is the investment rate on TreasuryDirect?+
The investment rate shown in Treasury bill auction results is the bond equivalent yield. It uses the formulas in 31 CFR Part 356, Appendix B, including the semiannual-compounding version for bills longer than half a year.
How is money market yield different from BEY?+
Both divide the gain by the purchase price, but the money market yield annualises with a 360-day year and BEY uses 365. Money market yield is the convention for CDs and other money market instruments in many markets.
Should I compare a T-bill BEY with a savings account APY?+
For the closest comparison use the effective annual yield, which assumes you reinvest at the same rate, against the APY. BEY is the right comparison against bond and note yields.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.