2026-09-22 7 min read

Treasury Bond Calculator

Long Treasury price with sovereign backing for a treasury bond. Live calculator with worked steps, charts and formulas.

Calculator

Face (Par) Value Help

Principal repaid at maturity, usually $1,000.

Annual Coupon Rate(%) Help

Interest paid on face value each year.

Yield to Maturity(%) Help

Market discount rate used to price the bond.

Years to Maturity(years)

years

Coupon Frequency

This treasury & government calculator runs on standard bond mathematics: coupons and face value discounted at the market yield with 2 payment(s) per year. Money is calculated at full precision and rounded only for display.

Results

Caution

Bond Price (Clean)

$960

Trades at a discount — market yield beats the coupon.

Coupon Each Period

$23

Annual Coupon Income

$45

Discount Under Par

$40

Current Yield at This Price

4.69%

Coupon Periods

Live results update as you type — currently showing bond price (clean) of $960. Replace the defaults with your own quote for an exact comparison.

Visualizations

Cash Received Each Year

45Coupons

1,000Principal at maturity

Price vs Par

Price96%

Par difference4%

Formula

Long Treasury (20–30y) priced like any coupon bond; interest exempt from state/local tax.

P = Σ C/(1+r)ⁱ + Face/(1+r)ⁿ

Variables

Symbol	Name	Unit	Description
P	Bond price (clean)	currency	Present value of coupons plus face at the market yield
C	Coupon per period	currency	Face × coupon ÷ frequency
r	Periodic yield	decimal	Annual YTM ÷ payments per year
n	Periods to maturity	count	Years × payments per year

Explanation

Long-bond valuation with sovereign backing.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Compute the coupon paid each period from the annual rate.

Coupon = Face × Coupon ÷ Frequency

Face:$1,000

Coupon:4.50%

Frequency:2

Result: $22.50 per period

Step 2

Count the coupon periods to maturity.

n = Years × Frequency

Years:30

Frequency:2

Result: 60 periods

Step 3

Discount every coupon plus the face value at the periodic yield.

Price = Σ Coupon/(1+r)ⁱ + Face/(1+r)ⁿ

Periodic yield:2.3750%

Intermediate: r = 4.75% ÷ 2

Result: Bond price = $960.24

Final Answer

$960

Worked Examples

See how the calculator works with different scenarios.

Scenario

The treasury bond calculator run on the values above, showing the full calculation path rather than only the answer.

Inputs

Face (Par) Value:1000

Annual Coupon Rate:4.5

Yield to Maturity:4.75

Years to Maturity:30

Calculation

1. Compute the coupon paid each period from the annual rate. → $22.50 per period 2. Count the coupon periods to maturity. → 60 periods 3. Discount every coupon plus the face value at the periodic yield. → Bond price = $960.24

Result

Bond Price (Clean): $960

Interpretation

Treasury (long bond, backed by U.S. government): Clean price $960.24 on $1,000 par (-$39.76 discount); current yield 4.69%. Exempt from state/local tax.

Understanding Your Result

Your Result: Bond Price (Clean): $960

Typical range: At 4.75% the 4.50% coupon prices below par. A 1-point yield move shifts this bond roughly 16.08% the other way.

What This Means

Long-bond valuation with sovereign backing.

Why It Matters

Treasury (long bond, backed by U.S. government): Clean price $960.24 on $1,000 par (-$39.76 discount); current yield 4.69%. Exempt from state/local tax.

Professional Interpretation

Treasury (long bond, backed by U.S. government): Clean price $960.24 on $1,000 par (-$39.76 discount); current yield 4.69%. Exempt from state/local tax.

How this is calculated

Long Treasury (20–30y) priced like any coupon bond; interest exempt from state/local tax.

What drives the result

T-Bills are sold at a discount with no coupons; notes and bonds pay coupons. Municipal interest is typically federal-tax exempt, so compare on a taxable-equivalent basis. Savings bonds (I and EE) accrue or composite with inflation and reward holding to term.

Recommendations

•Compare bonds by yield to maturity, never by coupon alone.
•Confirm clean vs dirty price before settling between coupon dates.
•Treasury interest is exempt from state and local income tax.

Educational Content

Introduction

Sovereign and government-linked bonds (Treasuries, T-Bills, municipals, savings bonds) share one trait: the credit backstop is a government. Pricing still follows present value, but tax treatment, auction mechanics and inflation linkage change the comparison.

Concept Explanation

Applications

▸Parking cash in T-Bills versus a money-market fund after tax

▸Choosing municipal versus corporate bonds in a high tax bracket

▸Holding I Bonds as an inflation hedge or EE Bonds for a 20-year double

▸Rolling Treasury auctions into a cash ladder

Benefits

•Puts discount, coupon and tax-exempt structures on one comparable basis
•Converts muni yields to taxable-equivalent hurdles
•Shows T-Bill discount versus investment (bond-equivalent) yield
•Separates real yield from inflation compensation on linkers

Limitations

•State-tax and AMT treatment varies by issue and domicile
•Auction prices move between announcement and settlement
•CPI linkage lags actual inflation prints by months
•Early redemption penalties (savings bonds) change realized returns

Best Practices

•Compare T-Bills to CDs on an after-tax, same-day-count basis
•Rerun muni math at your exact marginal bracket
•Hold savings bonds to their guarantee dates (12 months minimum, 20 years for EE doubling)
•Track CPI reset dates for I Bonds and TIPS

Common Misconceptions

Myth: Treasuries are risk-free in every sense

Truth: Credit risk is minimal, but price risk from rate moves and inflation risk on nominal bonds remain.

Myth: A muni always beats a corporate

Truth: Only above a break-even bracket. Below it, the taxable bond wins after tax.

Practical Tips

•STRIPS separate coupons for zero-like exposure.

Common Mistakes

Ignoring inflation on nominals

Compare TIPS real yields for purchasing-power view.

Assumptions

This calculator makes the following assumptions to provide estimates:

Semiannual coupons: Standard Treasury convention.

Limitations

Be aware of these limitations when using this calculator:

Limitation: State-tax and AMT treatment varies by issue and domicile

Limitation: Auction prices move between announcement and settlement

Limitation: CPI linkage lags actual inflation prints by months

Limitation: Early redemption penalties (savings bonds) change realized returns

Frequently Asked Questions

Answers to common questions about this calculator.

Why do long Treasuries swing so much?

Duration near 15–20 years: a 1% move shifts price ~15–20%.

Who uses the treasury bond calculator?

It is used by investors comparing treasury bond options, by advisers checking a quote before a client commits, and by planners sizing contributions for a goal. It sits in the Treasury & Government group of the Bonds & Fixed Income section of Atlascalcs.

How accurate is the treasury bond calculator?

Every figure follows directly from the inputs using standard bond mathematics, so it is accurate to the quality of the values you enter. Dealer quotes round to cents and apply day-count conventions, so expect pennies of difference on accrued interest and settlement figures.

How current are the yields used here?

The calculator uses the figures you enter, so update the yield to your dealer quote or auction result. Market yields move intraday; ratio and tax thresholds follow the conventions in the references.

Does rounding change the results?

All math runs at full precision and rounds only for display. Dealers round to cents and apply day-count conventions, so expect pennies of difference on accrued interest.

Should I compare coupons or yields?

Always yields (YTM for total return, current yield for income). Two bonds with different coupons price identically at the same YTM.

What should I have ready before buying?

Face, coupon, maturity, frequency, price or yield, settlement date, tax bracket and any call or conversion terms. With those, every figure here ties to a quote.

Related Calculators

Explore more calculators related to this topic.

Related Guides

Deepen your understanding with these educational resources.

Understanding bond pricing and yield to maturity

Coupons, discounting, and why price moves opposite the yield.

Building a bond ladder

Stagger maturities to collect income and reduce rate risk.

Tax implications of bond income

How Treasury, municipal, and corporate bond interest are taxed.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Par (Face) Value: Principal repaid at maturity, usually $1,000 per bond.
Coupon Rate: Annual interest rate paid on face value, split across the payment frequency.
Yield to Maturity: Total return holding to maturity with coupons reinvested at that rate.
Duration: Weighted-average time to cash flows (Macaulay) and price sensitivity (modified).

Authoritative References

Trusted sources and standards referenced by this calculator.

SEC — Investor.gov: Bonds TreasuryDirect — U.S. Government Bonds TreasuryDirect — TIPS FINRA — Learn About Bonds SIFMA — U.S. Fixed Income Research Federal Reserve — Treasury yields (H.15)

Applicable Standards

Present-value pricing with periodic compounding at the quoted yieldYTM solved numerically (bisection) to full precision; display rounded onlyT-Bill bank discount on 360 days; investment yield on 365 daysMoney rounded for display only; all calculations run at full precision

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Page Information

Last Updated:

2026-09-22

Version:

2.0.0

References:

License:

Free to use for educational and professional purposes.