Fidamen

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.

Updated Nov 8, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record 138a1bc9b7ac • Reviewed by Fidamen Standards Committee

Compute the present value (market price) of a zero-coupon bond given face value, annual nominal yield and compounding frequency.

Inputs

Results

Updates as you type

Purchase price

$863.84

OutputValueUnit
Purchase price$863.84—
Primary result$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).

F.A.Q.

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

Further resources

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: 138a1bc9b7ac

What changed (latest)

v1.0.0 • 2025-11-08 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Public QA status

PASS — golden 25 + edge 120

Last run: 2026-01-23 • Run: golden-edge-2026-01-23

Engine

v1.0.0

Data

Baseline (no external datasets)

Content

v1.0.0

UI

v1.0.0

Governance

Last updated: Nov 8, 2025

Reviewed by: Fidamen Standards Committee (Review board)

Credentials: Internal QA

Risk level: low

Reviewer profile (entity)

Fidamen Standards Committee

Review board

Internal QA

Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person

Semantic versioning

  • MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
  • MINOR: New features or fields that do not change existing outputs for the same inputs.
  • PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.

Review protocol

  • Verify formulas and unit definitions against primary standards or datasets.
  • Run golden-case regression suite and edge-case suite.
  • Record reviewer sign-off with credentials and scope.
  • Document assumptions, limitations, and jurisdiction applicability.

Assumptions & limitations

  • Uses exact unit definitions from the Fidamen conversion library.
  • Internal calculations use double precision; display rounding follows the unit's configured decimal places.
  • Not a substitute for calibrated instruments in regulated contexts.
  • Jurisdiction-specific rules may require official guidance.

Change log

v1.0.0 • 2025-11-08 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: e925462cb9f7