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Treasury Bill Yield CalculatorDiscount Yield, Money Market Yield and BEY

What do these figures come to once the work is shown?

Bank discount yield, money market yield, bond-equivalent yield and effective annual yield from a bill price, face value and days to maturity.

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Your figures
Example figuresIllustrative only. Type over them with your own.
Bond-equivalent yield
5.08%
Treasury investment rate: yield on price, comparable with coupon bonds
Bank discount yield
4.95%
Money market yield
5.01%
Drawn to one scale
Bond-equivalent yield5.08%
Bank discount yield4.95%
Money market yield5.01%
Effective annual yield5.17%
Holding period return1.27%
All results
MeasureResult
Bond-equivalent yield5.08%
Bank discount yield4.95%
Money market yield5.01%
Effective annual yield5.17%
Dollar discount earned$125
Holding period return1.27%
How this was worked out
Work shownrecomputed as you type
Bank discount yield = (face - price) / face x 360 / days
Money market yield = (face - price) / price x 360 / days
Bond-equivalent yield, half a year or less: (100 - P) / P x y / r
Over half a year: solve P[1 + (r - y/2)(i/y)](1 + i/2) = 100 for i
P = price per 100 of face, r = days to maturity, y = 365 or 366
Effective annual yield = (face / price)^(365 / days) - 1

Illustrative arithmetic on the figures you enter. Check the result against your firm's methodology before relying on it.

The formulas

  • Bank discount yield = (face - price) / face x 360 / days
  • Money market yield = (face - price) / price x 360 / days
  • Bond-equivalent yield, half a year or less: (100 - P) / P x y / r
  • Over half a year: solve P[1 + (r - y/2)(i/y)](1 + i/2) = 100 for i
  • P = price per 100 of face, r = days to maturity, y = 365 or 366
  • Effective annual yield = (face / price)^(365 / days) - 1

How it works

Treasury bills pay no coupon. TreasuryDirect states that bills are sold at a discount or at par, and you are paid face value at maturity, so the discount is the return. Treasury auctions bills on a discount rate basis, which divides the discount by face value and uses a 360-day year. That understates the return on the money invested.

The bond-equivalent yield, which Treasury calls the investment rate or coupon-equivalent yield, divides by the price paid and uses the days in the year after the issue date: 365, or 366 when that year contains February 29. For bills over half a year, the federal formula in 31 CFR Part 356 adds the coupon a note would pay at six months and is solved as a quadratic. The money market yield divides by price on a 360-day year, the convention for other money market instruments.

Illustrative figures only. Check the result against your firm's methodology before relying on it.

Common questions

Why is the discount yield the lowest figure?

It divides by face value, which is larger than the price, and uses a 360-day year.

Which yield compares with a savings account APY?

The effective annual yield, which assumes you roll the bill at the same rate all year.

Is T-bill interest taxed?

Yes, federally. TreasuryDirect states that federal tax is due on the interest and no state or local tax applies. IRS Publication 550 says the same for Treasury bills, notes and bonds.

Sources

Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.

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