Bond Equivalent Yield Calculator
Calculate the bond equivalent yield (BEY) of a discount instrument like a T-bill, annualizing the return on a 365-day basis. Enter the face value, purchase price, and days to maturity to get the annualized yield.
Formula
BEY = ((Face Value − Price) ÷ Price) × (365 ÷ Days to Maturity)
- BEY annualizes the return on a security bought at a discount and redeemed at face value.
- It takes the gain (face − price) as a fraction of price, then scales it to a full year using 365 ÷ days to maturity.
- Using 365 days makes it comparable to coupon-bond yields, unlike the 360-day bank discount rate.
- It assumes you hold the instrument to maturity and there are no coupon payments in between.
- A larger discount or a shorter maturity raises the annualized yield.
$1,000 bill, bought at $970, 180 days
Inputs
- Face Value: 1000
- Purchase Price: 970
- Days to Maturity: 180
Gain = 30 ÷ 970 = 3.09%. Annualized: 3.09% × (365 ÷ 180) ≈ 6.27% bond equivalent yield.
Frequently asked questions
What is bond equivalent yield?
BEY is the annualized return on a discount security, expressed on a 365-day basis so it can be compared with coupon-bearing bonds.
How is BEY different from the discount rate?
The bank discount rate uses face value and a 360-day year; BEY uses purchase price and 365 days, giving a slightly higher figure.
When is BEY used?
It is commonly used to quote yields on Treasury bills and other zero-coupon, short-term instruments sold at a discount.
Does BEY assume reinvestment?
No. It is a simple annualization of the holding-period return and does not compound or assume reinvested proceeds.
Why does a shorter maturity raise the yield?
The same percentage gain earned over fewer days annualizes to a higher rate when scaled up to a full year.