Zero Coupon Bond Calculator
This calculator provides multiple workflows for zero-coupon bonds: compute price from an annual nominal yield, infer yield from a given price, and convert nominal yield to effective annual yield. It supports variable compounding frequencies so results match commonly used market conventions.
Use the 'Price from Annual Yield' method when you know the bond's face value, years to maturity and the required nominal annual yield. Use 'Yield from Price' when you have a market price and need the implied yield. Use 'Effective Annual Yield' to compare yields with different compounding conventions.
Compute the present value (market price) of a zero-coupon bond given face value, annual nominal yield and compounding frequency.
Inputs
Results
Purchase price
$863.84
| Output | Value | Unit |
|---|---|---|
| Purchase price | $863.84 | — |
Visualization
Methodology
All formulas use present-value mathematics for a single future cash flow: price = face_value / (1 + periodic_y)^(periods). Periodic yield and total periods are determined by the selected compounding frequency.
When inferring yield from a price, the calculator solves for the periodic rate by taking the nth root: periodic_y = (face_value / price)^(1/n) - 1, then annualizes by multiplying by the compounding frequency to provide a nominal annual rate.
Effective annual yield is calculated from the nominal rate using standard compounding conversion: effective = (1 + nominal/periods)^(periods) - 1.
Worked examples
Example 1 — Price from yield: Face value 1,000; annual yield 5%; annual compounding; 3 years → Price = 1000 / (1.05)^3 = 863.84 (approx).
Example 2 — Yield from price: Face value 1,000; price 800; annual compounding; 5 years → periodic_y = (1000/800)^(1/5)-1 = 0.0443; annual nominal ≈ 4.43%.
Example 3 — Effective yield: Nominal 6% with semiannual compounding → Effective = (1 + 0.06/2)^2 - 1 = 6.0900% (approx).
Expert Q&A
Which compounding frequency should I use?
Choose the frequency that matches market conventions or the bond documentation. If the bond is quoted on a semiannual basis, select semiannual. Use effective yield to compare different conventions on a like-for-like basis.
Why do results differ between nominal and effective yields?
Nominal yield is expressed without accounting for intra-year compounding; effective yield includes the effect of compounding and therefore is higher when compounding occurs more than once per year.
How accurate are the results?
Results use floating-point arithmetic and standard mathematical functions. Expect small rounding differences due to IEEE 754 floating-point behavior. For regulatory or large-scale financial computations, validate against high-precision libraries or audited systems and document tolerance thresholds.
Can I use this for bonds with multiple cash flows?
No. This tool is specifically for zero-coupon bonds that deliver a single known cash flow at maturity. For coupon-paying bonds, use a multi-cash-flow bond valuation tool.
Sources & citations
- NIST — Computer Security and Software Engineering guidance — https://csrc.nist.gov/publications
- ISO — Quality management (ISO 9001 overview) — https://www.iso.org/iso-9001-quality-management.html
- IEEE 754 — Standard for Floating-Point Arithmetic — https://standards.ieee.org/standard/754-2019.html
- OSHA — Laws and Regulations — https://www.osha.gov/laws-regs