Treasury
Zero-Coupon Bond Calculator
Discount a single payment at maturity to estimate a zero-coupon bond’s present value. The calculator also shows the purchase discount, percentage gain if held to maturity, modified duration, and DV01.
Zero-coupon bond calculator
A clean present-value model before accrued tax, fees, and credit adjustments.
Zero-coupon bond price formula
Price equals face value ÷ (1 + yield ÷ frequency)years × frequency. A $1,000 payment due in ten years is worth less today because the market yield discounts that future cash flow. A higher required yield lowers the price; a longer maturity generally increases the discount.
Purchase discount and maturity gain
The purchase discount is face value minus estimated price. Maturity gain is the increase from price to face value as a percentage of price. It is not an annualized return and assumes the issuer makes the payment at maturity. Selling earlier can produce a gain or loss as prevailing yields and credit conditions change.
Duration and DV01
A zero-coupon bond’s Macaulay duration equals its time to maturity because all cash arrives at the end. Modified duration adjusts that time measure for yield and compounding. DV01 uses modified duration to estimate the dollar price change for a one-basis-point yield move. Both are local approximations; larger moves introduce curvature that duration alone does not capture.
Taxes, credit, and market prices
Some zero-coupon securities may generate taxable imputed interest before cash is received. Credit risk, liquidity, settlement, day-count rules, and transaction costs can also make a quoted market price differ from this simplified result. Treasury STRIPS have different credit characteristics from corporate zero-coupon bonds.
Learn how Treasury principal and interest components are separated through the official Treasury STRIPS overview. This calculator is educational and is not investment or tax advice.
Frequently asked questions
How do you price a zero-coupon bond?
Discount the face value by the market yield for the number of compounding periods remaining until maturity.
Does a zero-coupon bond pay interest?
It does not make periodic coupon payments. The investor’s return generally comes from buying below face value and receiving face value at maturity, subject to credit and tax considerations.