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Zero Coupon Bond Calculator
A zero coupon bond pays no interest along the way; you buy it at a discount and receive the face value at maturity. Enter any three of price, yield, face value and term to solve for the fourth, with your choice of compounding.
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Bond
$
$
%
years
Decimals allowed, e.g. 7.5.
Enter your values to see the result.
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How to use the Zero Coupon Bond Calculator
- Choose what to solve for: price, yield, face value or years.
- Enter the other three values: face value, price, annual yield and years to maturity as needed.
- Pick the compounding. US zero coupon bonds and Treasury STRIPS are usually quoted with semi-annual compounding.
- Read the result along with the effective annual yield, total return and duration.
- Check the accretion schedule to see how much the bond's value grows each year.
Zero coupon bond formulas
| Solve for | Periodic compounding (m per year) | Continuous compounding |
|---|---|---|
| Price | P = F ÷ (1 + y/m)mT | P = F × e−yT |
| Yield | y = m × [(F ÷ P)1/(mT) − 1] | y = ln(F ÷ P) ÷ T |
| Face value | F = P × (1 + y/m)mT | F = P × eyT |
| Years | T = ln(F ÷ P) ÷ [m × ln(1 + y/m)] | T = ln(F ÷ P) ÷ y |
Price of a 1,000 zero coupon bond (semi-annual compounding)
| Years | 3% yield | 4% yield | 5% yield | 6% yield |
|---|---|---|---|---|
| 1 | 970.66 | 961.17 | 951.81 | 942.60 |
| 5 | 861.67 | 820.35 | 781.20 | 744.09 |
| 10 | 742.47 | 672.97 | 610.27 | 553.68 |
| 20 | 551.26 | 452.89 | 372.43 | 306.56 |
| 30 | 409.30 | 304.78 | 227.28 | 169.73 |
The longer the term and the higher the yield, the deeper the discount. A 30-year zero at 6% costs well under a fifth of its face value.
Tips
- Compare yields on the same basis. 4.5% compounded semi-annually is an effective annual yield of about 4.55%. Use the effective yield to compare with CDs or annual-pay bonds.
- Hold to maturity for a known return. If you keep the bond to maturity, your return is locked in at purchase; selling earlier exposes you to price changes.
- Plan for a target date. Zeros are useful for funding a known future expense, such as tuition, because the maturity value is fixed. Use the face-value mode to see what an investment grows to.
Frequently asked questions
How do you calculate the price of a zero coupon bond?
Price = Face ÷ (1 + y/m)^(m × T), where y is the annual yield, m the compounding periods per year and T the years to maturity. A 1,000 bond maturing in 10 years at a 4.5% yield with semi-annual compounding costs 1,000 ÷ 1.0225^20 = 640.82.
How do you find the yield of a zero coupon bond?
Rearrange the price formula: y = m × [(Face ÷ Price)^(1 ÷ (m × T)) − 1]. With annual compounding this is simply (Face ÷ Price)^(1/T) − 1. With continuous compounding it is ln(Face ÷ Price) ÷ T.
Why are zero coupon bonds so sensitive to interest rates?
All of the cash arrives at maturity, so the Macaulay duration equals the full term. A 20-year zero has a duration of 20 years, much longer than a 20-year coupon bond, so its price moves more for the same change in yield.
Do I pay tax on a zero coupon bond before maturity?
In the US, taxable zero coupon bonds usually generate imputed interest (original issue discount) each year even though no cash is paid, often called phantom income. The accretion schedule shows the constant-yield growth in value, which is the basis for that calculation; consult a tax professional for your situation.
What compounding should I use?
US Treasury STRIPS and most US zero coupon bonds are quoted on a semi-annual bond-equivalent basis. Use annual compounding for many international bonds, and continuous compounding for finance theory and derivatives pricing. The effective annual yield lets you compare them.
What is the difference between a zero coupon bond and a Treasury bill?
Both are sold at a discount and pay face value at maturity. Treasury bills mature in a year or less and are quoted with a bank discount rate, while zero coupon bonds and STRIPS can run for decades and are quoted by yield to maturity.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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