Zero Coupon Bond Calculator
Calculate a zero-coupon bond's price from its yield, or its yield to maturity from its price, with a selectable compounding frequency (annual, semi-annual, quarterly, monthly, daily, or continuous) — plus discount amount, effective annual yield, and a year-by-year accreted-value schedule.
Input
Output
| Metric | Value |
|---|---|
| No data yet | |
| Year | Accreted Value |
|---|---|
| No data yet | |
Guides
What is a zero-coupon bond?
A zero-coupon bond pays no periodic interest at all. Instead, you buy it below its face value and receive the full face value back at maturity — the entire return is that single discount. U.S. Treasury STRIPS, EE savings bonds, and many long-dated college-savings or retirement-target bonds work this way, which is why they're priced with a single present-value formula instead of the coupon-schedule math a regular bond needs.
How this tool works
- Choose whether you're solving for Bond Price (you know the yield and want the price) or Yield to Maturity (you know the price and want the implied yield).
- Enter the face value — what the bond pays at maturity.
- Enter either the annual yield (price mode) or the current market price (yield mode), whichever the calculator is solving for.
- Set years to maturity and a compounding frequency — annual, semi-annual, quarterly, monthly, daily, or continuous.
- Choose a currency for the formatted output.
The Summary table shows the solved price or yield, the discount amount and percentage, total return over the full term, the effective annual yield (compounding-frequency-independent, so it's directly comparable across bonds quoted with different frequencies), and Macaulay duration — which for a zero-coupon bond always equals its years to maturity, since there's only one cash flow. The Year-by-Year Accreted Value table shows how the bond's present value climbs from the purchase price up to face value as each year of discounting falls away, downloadable as CSV.
The math
A zero-coupon bond's price is the present value of its single future payoff:
- Periodic compounding:
P = F / (1 + r/n)^(n·t) - Continuous compounding:
P = F · e^(−r·t)
where F is face value, r is the annual yield, n is compounding periods per year, and t is years to maturity. Solving the same relationship for r instead of P gives yield to maturity:
- Periodic:
r = n · [(F/P)^(1/(n·t)) − 1] - Continuous:
r = ln(F/P) / t
Why compounding frequency matters
The same face value, price, and term produce a different quoted yield depending on how often compounding is assumed to happen — daily compounding needs a slightly lower nominal rate than annual compounding to reach the same price, because it compounds more often. The effective annual yield in the summary strips that choice out, giving you a single number you can compare across bonds quoted with different compounding conventions.
Common uses
- Pricing a Treasury STRIP or zero-coupon municipal bond from a target yield
- Backing out the implied yield on a discount bond you're evaluating at its quoted market price
- Planning a target-date purchase (e.g. a college-savings zero) by solving for the price needed today to reach a known face value at a known date
For a coupon-paying bond's full yield breakdown, use the Bond Yield to Maturity Calculator. For a discount security's short-term money-market yield, use the Bond Equivalent Yield Calculator.
Privacy
This tool runs entirely in your browser. Your numbers are never uploaded to a server.
Use it from code
From 3 credits per callREST API
curl -X POST https://api.iotools.cloud/v1/tool/zero-coupon-bond-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"calcType": "price",
"faceValue": "1000",
"rate": "5",
"years": "10",
"compound": "1",
"currency": "USD"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `zero-coupon-bond-calculator` tool (Zero Coupon Bond Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.