Zero-Coupon Bond Price Calculator

Understanding the zero-coupon bond calculator — concept and principle

A zero-coupon bond pays no periodic interest. You buy it at a discount and receive the full face value at maturity; the difference is your return. Treasury STRIPS, many savings bonds and discount notes work this way. This calculator finds the price today for a given face value, yield and time to maturity, the discount from face value, the implied interest and the bond's Macaulay duration.

How it is calculated

• Price P = F ÷ (1 + y ÷ k)^(k × n), where F is the face value, y the annual yield, k the compounding periods per year (1 annual, 2 semi-annual, and so on) and n the years to maturity.
• Discount = 1 − P ÷ F.
• Implied interest = F − P.
• Macaulay duration = n, because the only cash flow arrives at maturity.

The principle

A single payment in the future is worth less today because money can earn a return in the meantime. Discounting asks: how much would I need to invest now at yield y, compounded k times a year, to grow to F by maturity? That amount is the fair price. Because all the value sits in one distant payment, a zero-coupon bond is more sensitive to interest-rate changes than a coupon bond of the same maturity: when yields rise, its price falls more. Its modified duration is n ÷ (1 + y ÷ k), so a 1-point rise in yield cuts the price by roughly that many percent.

Worked example

Default inputs: face value $10,000, yield 4.5%, 10 years, semi-annual compounding.

1. Rate per period: 4.5% ÷ 2 = 2.25%; periods: 2 × 10 = 20.
2. Price: 10,000 ÷ 1.0225²⁰ = $6,408.16.
3. Discount: 1 − 6,408.16 ÷ 10,000 = 35.92%.
4. Implied interest: 10,000 − 6,408.16 = $3,591.84.
5. Macaulay duration: 10 years.

With annual compounding the price would be about $6,439.28.

How to read the result

The longer the maturity and the higher the yield, the deeper the discount. Holding to maturity locks in the yield you bought at, barring default, but selling earlier exposes you to price changes. Long zeros are used to match a known future need, such as a tuition payment or a pension liability, because the payoff date and amount are fixed.

Common mistakes

• Mixing compounding conventions when comparing quotes.
• Forgetting that many tax systems tax the accrued discount each year even though no cash is paid.
• Underestimating price volatility for long maturities.
• Ignoring credit risk for corporate zeros.

Frequently asked questions

What is $10,000 due in 10 years worth at 4.5%?

About $6,408 with semi-annual compounding.

Are zero-coupon bonds taxed before maturity?

In many countries, including the US, the accrued discount is taxed yearly as "phantom income".

Why is duration equal to maturity?

Duration is the weighted average time of cash flows, and there is only one, at maturity.

Sources: Fabozzi, F. J., Bond Markets, Analysis, and Strategies · U.S. Department of the Treasury, TreasuryDirect, STRIPS