Bond Yield to Maturity Calculator

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Bond price:

Full price on a coupon date, using the same currency as face value.

Face value:

Principal repaid at maturity.

Annual coupon rate:

% / year

Enter 5 for a 5% stated coupon. Zero-coupon bonds may use 0.

Years to maturity:

years

Use a term containing whole coupon periods; 7.5 years works with semiannual coupons.

Coupon frequency:

Match the bond disclosure.

Yield precision:

The default is 4 decimals and changes display only.

Yield analysis

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Calculation method:

All displayed artifacts consume the same converged computation.

Price = Σ coupon / (1 + r)^t + face / (1 + r)^n

Nominal YTM = periodic rate × coupon frequency.
Effective annual yield = (1 + periodic rate)^frequency − 1.
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Assumes a fixed-rate bond priced on a coupon date; no accrued interest, calls, taxes, fees, or credit-loss modeling.

The chart renderer is unavailable. The same yield values remain available in the analysis and ledger.

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A bond can pay a fixed coupon and still offer a yield above or below that coupon rate. The difference comes from price. Buying below face value adds a gain when principal is repaid at maturity, while buying above face value creates a loss that offsets part of the coupon income. Price and yield therefore move in opposite directions.

Yield to maturity (YTM) expresses the discount rate that makes all scheduled coupon payments and the final principal repayment equal the bond's current full price. It is useful for comparing conventional fixed-rate bonds with different prices, coupon rates, and remaining terms on one annualized basis.

Coupon rate: Annual coupon cash divided by face value. It is fixed by the bond terms rather than by today's market price.
Current yield: Annual coupon cash divided by the price paid. It ignores the gain or loss between price and face value.
Yield to maturity: The discount rate implied by price when every scheduled payment is made and the bond is held to maturity.
Effective annual yield: The annual rate after compounding the solved periodic yield at the coupon frequency.

YTM is a comparison measure, not a promise of realized return. Selling early changes the price received. A call can end the cash-flow schedule sooner, missed payments can reduce return, and coupon reinvestment may occur at rates different from the solved yield. Taxes, fees, accrued interest, and inflation can also change the investor's outcome.

The convention matters as much as the number. A price quoted between coupon dates normally needs accrued-interest and day-count treatment. A coupon-date model is appropriate only when the entered price is a full price on a coupon date and the remaining term contains a whole number of payment periods.

How to Use This Tool:

Match the inputs to one conventional fixed-rate bond and one coupon-date valuation before comparing the resulting yields.

Enter the bond's full Bond price and Face value in the same currency. Use the price for the assumed coupon date rather than a clean price that excludes accrued interest.
Enter the stated Annual coupon rate as a percentage and choose the coupon frequency shown in the bond disclosure. A zero-coupon bond may use 0%.
Enter Years to maturity so it contains a whole number of the selected coupon periods. For example, 7.5 years is compatible with semiannual payments but not annual payments.
Select Yield precision for display, then read the nominal YTM together with the effective annual yield, current yield, and price residual. Changing precision does not change the solved rate.

Interpreting Results:

Nominal YTM is the conventional annual rate obtained by multiplying the periodic yield by the number of coupon payments per year. Annual effective yield compounds that periodic rate, so it will differ whenever payments occur more than once a year.

A price below face value usually produces a YTM above the coupon rate because maturity adds a price gain.
A price above face value usually produces a YTM below the coupon rate because maturity brings a price loss.
Current yield measures coupon cash against price only. Do not substitute it for YTM when the price differs materially from face value.
A near-zero Price residual shows that discounting the scheduled cash flows at the solved rate reproduces the entered price.

Before comparing securities, confirm that they use compatible price, compounding, settlement, call, credit, and tax conventions. A higher YTM can reflect higher risk rather than a better risk-adjusted opportunity.

Technical Details:

A conventional fixed-rate bond is a series of equal coupon payments followed by the final coupon plus face value. The periodic discount rate cannot usually be isolated with ordinary algebra, so it is found numerically by matching the present value of that cash-flow series to the entered price.

Formula Core:

The solved periodic rate r makes the discounted cash flows equal price P. The nominal and effective annual yields are then derived from the same periodic rate.

\begin{matrix} C & = & \frac{F \times q}{m} \\ P & = & \sum_{t = 1}^{N} \frac{C}{{(1 + r)}^{t}} + \frac{F}{{(1 + r)}^{N}} \\ y_{nominal} & = & m \times r \\ y_{effective} & = & {(1 + r)}^{m} - 1 \\ y_{current} & = & \frac{F \times q}{P} \end{matrix}

Bond yield formula symbols and conventions
Symbol	Meaning	Unit or rule
`P`	Entered full bond price	Same currency as face value
`F`	Face value repaid at maturity	Currency
`q`	Annual coupon rate	Entered percentage divided by 100
`m`	Coupon frequency	1, 2, or 4 payments per year
`N`	Complete remaining coupon periods	Years to maturity multiplied by `m`
`r`	Solved yield per coupon period	Decimal rate greater than -1

For a price of 950, face value of 1,000, 5% annual coupon, 10 years to maturity, and semiannual payments, each coupon is 25 and there are 20 periods. The solved periodic yield is about 2.8308445%, producing a nominal YTM of 5.6616891% and an effective annual yield of 5.7418259%.

Mechanism Core:

The solver brackets a periodic rate whose present value crosses the entered price, then performs 160 bisection steps. Bisection repeatedly halves the interval and keeps the half containing the price match. The final ledger reprices the cash flows at the midpoint and reports model price minus entered price as the residual.

Calculations retain full numeric precision. The selected 2, 4, or 6 decimal setting rounds displayed yield values only; it does not feed a rounded rate back into repricing.

Limitations:

This is an educational fixed-cash-flow estimate, not financial advice or a trade quotation.

The model assumes a fixed-rate bond priced in full on a coupon date, with scheduled coupons and principal paid exactly as entered.
Accrued interest, settlement dates, day-count conventions, odd first or last coupons, calls, puts, sinking funds, floating rates, inflation indexing, and credit losses are outside the calculation.
Taxes, commissions, bid-ask spreads, reinvestment rates, and sale price before maturity can make realized return differ from YTM.
Review the bond disclosure and compare yield to call or yield to worst when an early redemption right applies.

References:

Understanding Bond Yield and Return, Financial Industry Regulatory Authority, August 11, 2022.
Understanding Pricing and Interest Rates, U.S. Department of the Treasury.