About the Zero Coupon Bond Calculator
A zero-coupon bond pays no interest along the way. You buy it at a discount and receive the full face value at maturity; the difference is your return. Treasury STRIPS, municipal zeros and some corporate bonds work this way. This zero coupon bond calculator prices a zero from a required yield, and solves the yield to maturity implied by any market price you enter.
It is for investors matching a future expense such as tuition or a retirement date, students working through bond-pricing problems, and anyone comparing a zero with a coupon bond or a CD. The schedule shows the bond’s accreted value at the end of each year and the imputed (phantom) interest for that year under the constant-yield method.
Yields are annual rates compounded at the frequency you choose; US convention for zeros is semiannual, matching Treasury quotes. Prices assume a whole number of years and ignore taxes, fees and credit risk. In a taxable account, US holders generally owe tax each year on the accrued original issue discount even though no cash is paid.
With the default inputs, the bond price at required yield is $640.82. Change any value above to recalculate instantly.
How to use the zero coupon bond calculator
- 1Enter the face value you will receive at maturity.
- 2Enter the years until maturity.
- 3Enter the yield you require (or a current market yield) and the compounding convention.
- 4Optionally enter a quoted market price to see the yield it implies.
- 5Review the price, discount and the year-by-year imputed interest.
Formula and method
A zero-coupon bond’s price is simply the present value of its single payment: the face value discounted at the yield for the number of compounding periods to maturity. Solving the same equation for y gives the yield to maturity implied by a market price. Because the yield is compounded m times a year, a 4.5% semiannual yield means 2.25% every six months.
The accreted value V(t) = P × (1 + y/m)^(m·t) rises along a smooth curve from the purchase price to face value. Under the constant-yield method used for original issue discount, the imputed interest for a year is the increase in accreted value during that year, so it grows a little every year.
- P
- Price of the bond today
- F
- Face value paid at maturity
- y
- Annual yield to maturity (decimal)
- m
- Compounding periods per year
- T
- Years to maturity
Worked examples
$1,000 10-year zero at a 4.5% semiannual yield
Discounting $1,000 over 20 half-years at 2.25% gives 1,000 ÷ 1.0225^20 = $640.82. Year-one imputed interest is $640.82 × (1.0225² − 1) = $29.16. A quoted price of $620 implies a higher yield of about 4.84%.
College fund: $25,000 due in 18 years at 5% annual
At 5% compounded annually, $25,000 in 18 years is worth 25,000 ÷ 1.05^18 = $10,388 today. If you could buy it for $10,000, the yield would be about 5.22%.
$10,000 5-year zero, 4% compounded monthly
With 60 monthly periods at 0.3333%, the price is 10,000 ÷ (1 + 0.04/12)^60 = $8,190.03, and the first year accrues $333.67 of interest. A price of $8,000 implies 4.47%.
Frequently asked questions
How do you calculate the price of a zero-coupon bond?+
Divide the face value by (1 + y/m) raised to the number of compounding periods to maturity. A $1,000 zero maturing in 10 years at a 4.5% semiannual yield costs 1,000 ÷ 1.0225^20 = $640.82.
Do you pay tax on zero-coupon bonds before maturity?+
In the US, holders of taxable zeros generally must report the accrued original issue discount as interest income each year, even though no cash is received. Holding zeros in an IRA or buying tax-exempt municipal zeros avoids this phantom income.
Why are zero-coupon bonds more sensitive to interest rates?+
All of the cash arrives at maturity, so a zero’s duration equals its full term. A 10-year zero loses roughly 10% of its value for a one-percentage-point rise in yields, more than a 10-year coupon bond.
What are Treasury STRIPS?+
STRIPS are zero-coupon securities created by separating the interest and principal payments of Treasury notes and bonds. Each piece trades separately at a discount and pays its face amount on a single date.
Should I use semiannual or annual compounding?+
Use the convention of the yield you are given. US Treasury and corporate yields are quoted on a semiannual bond-equivalent basis, while many international markets and textbook problems use annual compounding.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.