What is the zero-coupon bond price formula?

Price = F ÷ (1 + r ÷ k)t × k, where F is the face value, r the annual yield, k compounding periods per year and t years to maturity.

Why are zero-coupon bonds sold at a discount?

Because they pay no interest, the only return is the difference between the purchase price and the face value.

What is the duration of a zero-coupon bond?

Its Macaulay duration equals its time to maturity.

Zero-Coupon Bond Price Formula

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Zero-Coupon Bond Price Calculator

A zero-coupon bond pays no interest along the way. The investor buys it at a discount and receives the full face value at maturity; the difference is the interest earned. Treasury bills, STRIPS, savings bonds and many corporate discount notes work this way. Because there is only one cash flow, the price is simply its present value: F ÷ (1 + r ÷ k)^{t × k}.

Formula

Price = F(1 + r ÷ k)^{t × k} Yield = k × [(FPrice)^{1/(t × k)} − 1]

Where

F: face value paid at maturity
r: annual yield (discount rate)
k: compounding periods per year (1 annual, 2 semi-annual)
t: years to maturity

Calculator

Face value (F)

Annual yield (r) (%)

Years to maturity (t)

Compounding

Result and step-by-step solution

Zero-coupon bond price

613.91

Buy at 613.91, receive 1,000.00 in 10 years: the 386.09 discount is the interest.

Growth factor
(1 + 0.05 ÷ 1)¹⁰ = 1.62889463
Discount the face value
1,000.001.62889463 = 613.91

How to use the formula

The compounding convention matters. Finance textbooks often use annual compounding, while US Treasury STRIPS and most bond-market quotes use semi-annual compounding (k = 2). The calculator lets you choose, so a 10-year zero at 5% costs 613.91 with annual compounding and 610.27 with semi-annual compounding.

Zeros are the purest form of interest-rate exposure: their duration equals their maturity, so long zeros move sharply when yields change. Taxes can also be awkward, because in many countries the accreting discount is taxed each year even though no cash is received. The pricing is identical to the present value formula; for bonds with coupons, see the bond price formula.

Frequently asked questions

What is the zero-coupon bond price formula?: Price = F ÷ (1 + r ÷ k)^{t × k}, where F is the face value, r the annual yield, k compounding periods per year and t years to maturity.
How do I find the yield of a zero-coupon bond?: Yield = k × [(F ÷ Price)^{1/(t × k)} − 1].
Why are zero-coupon bonds sold at a discount?: Because they pay no interest, the only return is the difference between the purchase price and the face value.
What is the duration of a zero-coupon bond?: Its Macaulay duration equals its time to maturity.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.