Bond equivalent yield calculator
Bills, commercial paper and other discount instruments pay no coupon: you buy below face value and get the face value at maturity. Their yield can be quoted in several ways, which makes them hard to compare. Enter the face value, the price you pay and the days to maturity to see the bond equivalent yield next to the bank discount yield, the money market yield, the effective annual yield and the return over the holding period.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the face value paid at maturity.
- Enter the purchase price.
- Enter the days to maturity.
- Bond equivalent yield (up to 182 days) = (F − P) ÷ P × 365 ÷ d
- Over 182 days: the root of a·x² + b·x + c = 0 with a = d ÷ 730 − 0.25, b = d ÷ 365, c = (P − F) ÷ P
- Bank discount yield = (F − P) ÷ F × 360 ÷ d
- Money market yield = (F − P) ÷ P × 360 ÷ d
- Effective annual yield = (F ÷ P)^(365 ÷ d) − 1
Worked example
A 90-day bill with a face value of 1,000 bought at 985:
- Discount 15.00, return over the 90 days 15 ÷ 985 = 1.5228 %.
- Bond equivalent yield = 1.5228 % × 365 ÷ 90 = 6.176 %.
- Bank discount yield 6 %, money market yield 6.0914 %, effective annual yield 6.3212 %.
A 30-day paper bought at 9,900 for 10,000 gives a bond equivalent yield of 12.2896 % and a discount yield of 12 %.
Tips
- Quotes for bills are often the discount yield; convert before comparing them with bond yields.
- Count calendar days from settlement to maturity.
- The price above face value means a negative yield; the calculator stops there.
Frequently asked questions
How do you calculate the bond equivalent yield?
For up to 182 days: BEY = (face − price) ÷ price × 365 ÷ days. A 90-day bill bought at 985 for 1,000 face gives 15 ÷ 985 × 365 ÷ 90 = 6.1760 %.
Why is it different from the discount yield?
The bank discount yield divides the discount by the face value and uses a 360-day year: 15 ÷ 1,000 × 360 ÷ 90 = 6 %. The bond equivalent yield divides by the price you actually pay and uses 365 days, so it is always higher.
What happens for terms over half a year?
Over 182 days the calculator finds the yield of a bond with semiannual coupons that would grow the price to face value in that time, by solving a quadratic equation. For a one-year bill at 95 per 100 it gives 2 × (√(100 ÷ 95) − 1) = 5.1957 %.
Which yield should I compare with a savings rate?
The effective annual yield, which assumes you reinvest at the same rate for a whole year. The bond equivalent yield is the one to compare with coupon bonds quoted with semiannual coupons.