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Bond Calculator

Model a coupon bond's yield to maturity, present-value price, duration, modified duration, convexity, and cash-flow schedule from its core bond terms.

Published

Yield to maturity
Yield to maturity
5.26%
Current price
$980.00
Duration
7.97 years
Modified duration
7.76
Convexity
73.1498
Rates +1%
-7.40%
Rates -1%
8.13%
Cash flow schedule
Period 1
$25.00 paymentPV $24.36
Period 2
$25.00 paymentPV $23.74
Period 3
$25.00 paymentPV $23.13
Period 4
$25.00 paymentPV $22.53
Period 5
$25.00 paymentPV $21.96
Period 6
$25.00 paymentPV $21.39
Period 7
$25.00 paymentPV $20.85
Period 8
$25.00 paymentPV $20.31
Period 9
$25.00 paymentPV $19.79
Period 10
$25.00 paymentPV $19.28
Period 11
$25.00 paymentPV $18.79
Period 12
$25.00 paymentPV $18.31
Period 13
$25.00 paymentPV $17.84
Period 14
$25.00 paymentPV $17.38
Period 15
$25.00 paymentPV $16.94
Period 16
$25.00 paymentPV $16.50
Period 17
$25.00 paymentPV $16.08
Period 18
$25.00 paymentPV $15.67
Period 19
$25.00 paymentPV $15.27
Period 20
$1,025.00 paymentPV $609.89

Uses 20 rounded coupon periods and the same Newton-Raphson YTM method as the original calculator.

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Results update as you type.

Bond Calculator

This bond calculator is the overview page for valuing a plain coupon bond from the inputs most investors actually see: face value, stated coupon rate, market price, remaining years, and payment frequency. The result is not just one yield. It solves yield to maturity, rebuilds the bond’s present-value price, lists the cash flows, and adds duration, modified duration, convexity, and simple rate shock estimates. Use it when you want one fixed-income snapshot before moving to the narrower bond price calculator, bond yield calculator, or yield to maturity calculator.

What this calculator measures

A bond is a contract for scheduled payments. Most coupon dates pay interest, and the maturity date pays the last coupon plus the face value. The calculator uses those promised cash flows to answer two questions. First, what annual yield makes the cash flows equal the market price entered in the form? Second, after that yield is solved, how sensitive is the modeled price to a change in yields?

That makes this page a valuation hub rather than a single-purpose coupon tool. If you only need the stated coupon from a payment amount, use the coupon rate calculator. If you only need annual coupon income divided by price, use the bond current yield calculator. Here, the market price is central: the same 5% coupon can be a high-yielding discount bond, a par bond, or a low-yielding premium bond depending on what you pay today.

Formula matched to the calculator

For each period, the coupon is the face value times the annual coupon rate, divided by payments per year:

coupon per period=face value×coupon ratepayments per year\text{coupon per period} = \frac{\text{face value} \times \text{coupon rate}}{\text{payments per year}}

The calculator rounds years to maturity times payments per year to get the number of coupon periods. It then solves the annual yield that makes this present-value equation equal the market price:

market price=∑t=1ncash flowt(1+annual yieldpayments per year)t\text{market price} = \sum_{t=1}^{n}\frac{\text{cash flow}_{t}}{\left(1 + \frac{\text{annual yield}}{\text{payments per year}}\right)^{t}}

The final cash flow includes the last coupon plus face value. After solving yield, Macaulay duration weights each period by the present value of its cash flow:

duration=∑t=1nt×present valuet∑t=1npresent valuet×payments per year\text{duration} = \frac{\sum_{t=1}^{n}t \times \text{present value}_{t}}{\sum_{t=1}^{n}\text{present value}_{t} \times \text{payments per year}}

Modified duration is:

modified duration=duration1+annual yieldpayments per year\text{modified duration} = \frac{\text{duration}}{1 + \frac{\text{annual yield}}{\text{payments per year}}}

Example

Use the default inputs: face value $1,000, coupon rate 5%, market price $980, 10 years to maturity, and 2 payments per year. The coupon per period is $25 because $1,000 · 5% ÷ 2 = $25. The calculator rounds 10 · 2 to 20 coupon periods.

It then solves the yield by iteration. The result is a nominal annual yield to maturity of 5.26%. At that yield, the present value of the 19 semiannual $25 coupons plus the final $1,025 payment comes back to $980.00, matching the entered market price. The duration is 7.97 years, modified duration is 7.76, and convexity is 73.1498. The rate-shock estimates show about -7.40% for a one-percentage-point yield increase and 8.13% for a one-percentage-point yield decrease, using the duration-plus-convexity approximation in the form component.

Price-yield relationship

Bond price and yield move inversely because the cash flows are fixed while the discount rate changes. If investors demand a higher yield for the same issuer, maturity, and coupon, the existing cash flows must be priced lower to compete. If market yields fall, older bonds with higher coupons can become more valuable and trade at a premium. The pull toward face value at maturity matters too: a discount bond can earn coupon income plus price accretion, while a premium bond can earn coupons but lose some principal value as maturity approaches.

Duration explains why the inverse relationship is not equally strong for every bond. A long bond with small coupons has more value tied to distant payments, so its price tends to swing more when yields move. A short bond or high-coupon bond returns cash sooner, so its duration is usually lower. Convexity refines the duration estimate because large yield changes are curved, not perfectly linear.

Tips for accurate inputs

  • Use the bond’s face value, not the price you paid, in the face value field.
  • Match the coupon frequency to the actual indenture or quote convention.
  • Enter years remaining, not the original maturity when the bond was issued.
  • Treat callable, putable, floating-rate, amortizing, and inflation-linked bonds cautiously because this page assumes scheduled fixed coupons and one face-value repayment.
  • Compare the solved YTM with current yield and coupon rate before assuming a discount bond is automatically attractive.

Informational note

This calculator is for education and scenario analysis. Market quotes can include dealer markups, bid-ask spreads, accrued interest, tax effects, credit risk, and call features. Treasury and agency securities, municipal bonds, and corporate bonds also use different quoting conventions. For savings and household planning outside bond valuation, the interest calculator and present value annuity calculator provide more general time-value-of-money context.

Sources

Frequently asked questions

What does this bond calculator solve?
It solves the yield to maturity that makes the entered market price equal the present value of the remaining coupons and final face value. It then uses that solved yield to report a model price, Macaulay duration, modified duration, convexity, rate shock estimates, and a period-by-period cash-flow schedule.
How is this page different from a bond price calculator?
A bond price calculator starts with a yield and discounts cash flows to find price. This hub starts with a market price and solves for the yield that explains that price, then adds duration and convexity so you can see how sensitive the same bond may be to yield changes.
Why do bond prices and yields move in opposite directions?
A bond promises the same scheduled cash flows regardless of the market yield you use to value them. When the required yield rises, each future coupon and principal payment is discounted more heavily, so present value falls. When the required yield falls, those same cash flows are worth more today.
What does duration mean in the result?
Duration is a time-weighted average of the bond's present-value cash flows, expressed in years. Longer duration usually means more price sensitivity to yield changes because more of the bond's value is received farther in the future. Modified duration converts that timing measure into an approximate price-change estimate.
Does this calculator include accrued interest or calls?
No. It models the scheduled coupon stream and final face value only. Broker quotes may separate clean price from accrued interest, and callable bonds can be redeemed before maturity. Taxes, liquidity, credit losses, transaction costs, and reinvestment rates also sit outside this educational calculation.

Related calculators

Bond Convexity CalculatorEstimate fixed-cash-flow bond convexity by repricing coupons and principal after matching up and down yield shocks, then use the curvature result with duration.Complete-Period Bond Yield WorksheetSolve nominal and effective annual yield for a stylized fixed-rate bond with an explicit whole number of complete coupon periods.Bond Price CalculatorDiscount a coupon bond's scheduled coupons and final face value at a chosen yield to maturity to estimate its fair present-value price.Effective Duration CalculatorEstimate a bond's effective duration by repricing fixed coupon cash flows after equal up and down yield shocks to measure interest-rate sensitivity.Bond Equivalent Yield CalculatorAnnualize a discount bond's price return on a 365-day basis with a precise BEY formula for bond price, face value, and days to maturity.Complete-Period Bond Yield CalculatorSolve nominal and effective annual bond yield from price and an explicit whole number of complete coupon periods.

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