Zero Coupon Bond Calculator
A zero coupon bond makes no periodic interest payments. Instead, it is sold at a significant discount to its face value and pays the full face value at maturity. The entire return comes from price appreciation. U.S. Treasury STRIPS, savings bonds, and many corporate zero coupon securities are purchased for education planning, retirement, or other goals where a known future lump sum is needed. This calculator computes the purchase price for a given yield, or the implied yield for a given price. It also shows the accreted value (book value) at any year between purchase and maturity, which is important for understanding the phantom income taxable each year in a taxable account. Duration is also shown: for zero coupon bonds, Macaulay duration always equals the time to maturity.
Zero coupon bond formulas
Price = Face Value / (1 + r/freq)^(years x freq)
Implied Yield = ((Face / Price)^(1 / years) - 1) x 100
Duration = Years to Maturity (always, for zero coupon bonds)
Annual Accretion = Price x ((1 + r/freq)^freq - 1)
Zero coupon bond uses
- Education funding: buy a zero coupon bond today to have a known amount at the child's college start date.
- Retirement planning: lock in a guaranteed future lump sum without reinvestment risk.
- Portfolio immunisation: match the duration of liabilities precisely, since duration equals maturity.
- U.S. Treasury STRIPS: created by separating the coupon and principal components of Treasury notes and bonds.
- Best held in tax-deferred accounts to avoid paying tax on phantom income each year.
Zero coupon bonds: frequently asked questions
What is a zero coupon bond?
A zero coupon bond pays no periodic interest. Instead, it is issued at a deep discount to face value and redeems at par at maturity. The investor's return comes entirely from the price appreciation between purchase price and face value. U.S. Treasury STRIPS are the most common example.
How is a zero coupon bond priced?
The price equals the present value of the face value discounted at the required yield: Price = Face Value / (1 + r)^n, where r is the periodic yield and n is the number of compounding periods. For annual compounding with a 5% yield and 10-year maturity on a $1,000 bond, the price is $1,000 / 1.05^10 = $613.91.
What is phantom income and how does it affect zero coupon bonds?
In taxable accounts, the IRS requires investors to report and pay tax each year on the imputed interest (the accretion of the discount), even though no cash is received. This phantom income tax liability makes zero coupon bonds particularly well-suited to tax-deferred accounts such as IRAs.
What is accreted value?
Accreted value is the current book value of the bond, reflecting the original purchase price plus the cumulative imputed interest to date. It increases each year toward the face value. At maturity, accreted value equals face value.
Are zero coupon bonds sensitive to interest rate changes?
Yes, more so than coupon bonds. Because all cash flow occurs at maturity, the Macaulay duration of a zero coupon bond equals its time to maturity, which is the maximum possible duration. This means zero coupon bonds experience the largest price swings for a given change in interest rates.
Official sources
- U.S. Treasury (STRIPS): Treasury STRIPS Program.
- IRS Publication 1212: Guide to Original Issue Discount (OID) Instruments.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.