Bond Equivalent Yield Calculator
Calculate the bond equivalent yield (BEY) for a discount security like a T-bill or commercial paper from its face value, purchase price, and days to maturity — plus discount rate, holding period return, effective annual yield, and a day-count-convention (360/365/366) comparison.
Input
Output
| Metric | Value |
|---|---|
| No data yet | |
| Day-Count Basis | Bank Discount Rate | Bond Equivalent Yield |
|---|---|---|
| No data yet | ||
Guides
What is bond equivalent yield?
Bond equivalent yield (BEY) converts the return on a discount security — a Treasury bill, commercial paper, or any instrument bought below face value and redeemed at face value on maturity — into an annualized percentage that can be compared against a coupon-paying bond quoted on a standard 365-day basis. Discount securities don't pay interest directly; the entire return is the gap between what you paid and what you get back, so BEY exists specifically to translate that gap into the same annualized language as everything else on a yield curve.
How this tool works
- Enter the security's face value — what it pays out at maturity.
- Enter the purchase price — what you actually paid for it today, which should be at or below face value for a discount security.
- Enter days to maturity — how many days from purchase to redemption.
- Choose a currency for the formatted output.
The Summary table shows the dollar discount, bond equivalent yield, bank discount rate, holding period return, effective annual yield, and a plain-language investment quality rating. The Yield by Day-Count Convention table recomputes the discount rate and BEY under 360-, 365-, and 366-day annualization bases side by side — the same trade, three different numbers, depending purely on which convention is applied.
The math
For face value F, purchase price P, and D days to maturity:
- Discount =
F − P - Holding period return =
(F − P) / P - Bank discount rate =
(F − P) / F × (360 / D)— the convention T-bills are quoted in, annualized on a 360-day basis and expressed as a fraction of face value rather than price paid - Bond equivalent yield =
(F − P) / P × (365 / D)— annualized on a 365-day basis and expressed as a fraction of the price actually paid, which is why BEY is always a bit higher than the bank discount rate on the same trade - Effective annual yield =
(1 + holding period return)^(365/D) − 1— compounds the holding-period return forward instead of just scaling it linearly, so it's the highest of the three annualized figures
Why the day-count convention matters
The bank discount rate and BEY don't just differ because of the 360- vs. 365-day divisor — they also divide by different bases (face value vs. purchase price), which is the larger source of the gap. The Yield by Day-Count Convention table isolates just the day-count effect by holding the discount-rate and BEY formulas fixed and swapping only the annualization basis (360/365/366), making it clear how much of a quoted yield is the trade itself versus the convention used to annualize it.
Common uses
- Converting a broker-quoted T-bill discount rate into a comparable BEY before ranking it against coupon bonds
- Checking commercial paper or banker's acceptance pricing against a target annualized return
- Verifying that a quoted yield used the day-count basis you expect
For a coupon-paying bond's full yield breakdown instead of a discount security, use the Bond Yield to Maturity Calculator. For a general compounding return on a lump sum, use the Compound Interest Calculator.
Privacy
This tool runs entirely in your browser. Your numbers are never uploaded to a server.
Use it from code
From 3 credits per callREST API
curl -X POST https://api.iotools.cloud/v1/tool/bond-equivalent-yield-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"faceValue": "10000",
"purchasePrice": "9800",
"daysToMaturity": "182",
"currency": "USD"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `bond-equivalent-yield-calculator` tool (Bond Equivalent Yield Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.