Short answer
Zero-coupon bond price = face value ÷ (1 + y/m)^n. A $1,000 zero maturing in 10 years at a 4% yield, compounded semi-annually, is $672.97.
1. The formula
Price = F ÷ (1 + y/m)n, where F is face value, y is the annual yield, m is compounding periods per year and n = years × m.
2. Worked example
| Compounding | Calculation | Price |
|---|---|---|
| Semi-annual | $1,000 ÷ 1.0220 | $672.97 |
| Annual | $1,000 ÷ 1.0410 | $675.56 |
The $327.03 difference between price and face value is your whole return, earned as the price accretes toward $1,000.
3. Why zeros are so sensitive to rates
With no coupons, every dollar arrives at maturity. At a 4.5% yield, a 10-year zero costs $640.82 and has a modified duration of 9.78, compared with 7.98 for a 10-year 4.5% coupon bond at par.
4. Using the calculator
Set the coupon rate to 0%, enter face value, yield and years, and the ledger shows the price rising toward par each period.
5. Frequently asked questions
How do I price a zero-coupon bond?expand_more
Divide the face value by (1 + yield per period) raised to the number of periods.
Why is a zero-coupon bond cheaper than its face value?expand_more
Because you receive nothing until maturity, so the face value is discounted for the time and the yield you require.
Does compounding frequency matter for a zero?expand_more
Slightly. Semi-annual compounding gives a slightly lower price than annual at the same quoted yield.
Are zero-coupon bonds riskier?expand_more
They are more sensitive to rate changes for their maturity because all cash flows come at the end.