Bond Price & Yield-to-Maturity Calculator
Financial Calculators
Price bonds or solve YTM from price, with optional single-call YTC/YTW and federal tax-equivalent yield, plus duration, convexity, and cash-flow details.
Cash Flow Schedule
| Period | Time (yr) | Cash Flow | Present Value |
|---|---|---|---|
| 1 | 0.50 | $25.00 | $24.27 |
| 2 | 1.00 | $25.00 | $23.56 |
| 3 | 1.50 | $25.00 | $22.88 |
| 4 | 2.00 | $25.00 | $22.21 |
| 5 | 2.50 | $25.00 | $21.57 |
| 6 | 3.00 | $25.00 | $20.94 |
| 7 | 3.50 | $25.00 | $20.33 |
| 8 | 4.00 | $25.00 | $19.74 |
| 9 | 4.50 | $25.00 | $19.16 |
| 10 | 5.00 | $25.00 | $18.60 |
| X | Cash Flow | Present Value |
|---|---|---|
| P1 | $25.00 | $24.27 |
| P2 | $25.00 | $23.56 |
| P3 | $25.00 | $22.88 |
| P4 | $25.00 | $22.21 |
| P5 | $25.00 | $21.57 |
| P6 | $25.00 | $20.94 |
| P7 | $25.00 | $20.33 |
| P8 | $25.00 | $19.74 |
| P9 | $25.00 | $19.16 |
| P10 | $25.00 | $18.60 |
| P11 | $25.00 | $18.06 |
| P12 | $25.00 | $17.53 |
| P13 | $25.00 | $17.02 |
| P14 | $25.00 | $16.53 |
| P15 | $25.00 | $16.05 |
| P16 | $25.00 | $15.58 |
| P17 | $25.00 | $15.13 |
| P18 | $25.00 | $14.68 |
| P19 | $25.00 | $14.26 |
| P20 | $1,025.00 | $567.52 |
How to use this tool
- Choose mode. Select "Solve Price" to calculate a bond price from YTM, or "Solve YTM" to find the yield given a price.
- Enter bond parameters. Input the face value, coupon rate %, coupon frequency, and years to maturity.
- Enter price or YTM. Enter either the current price (Solve YTM mode) or the yield-to-maturity % (Solve Price mode).
- Review results. See the computed price or YTM, current yield, duration, convexity, and maturity cash-flow schedule. Optionally enable one call date for YTC/YTW or enter your federal marginal rate for a federal-only tax-equivalent yield.
Bond pricing formula
The fair price of a bond is the present value of all future cash flows discounted at the yield-to-maturity:
Price = Σ [C / (1 + y/n)^t] + F / (1 + y/n)^N
where C is the periodic coupon, y is the annual YTM, n is the coupon frequency (payments per year), F is the face value, t runs from 1 to N, and N is the total number of coupon periods.
Solving for yield-to-maturity
There is no closed-form solution for YTM. This calculator uses Newton-Raphson iteration with a bisection fallback to find the yield that equates the present value of all cash flows with the market price. It assumes regular coupon periods and does not account for accrued interest or settlement between coupon dates.
Optional yield to call and yield to worst
Enable Callable bond to enter one years-to-call value and a call price. The calculator rounds the call date to whole coupon periods, discounts coupons through that period, and treats the final cash flow as the coupon plus the call price. Yield to call (YTC) is solved from the current price using those cash flows. Yield to worst (YTW) is shown as the lower of the maturity YTM and this modeled YTC.
This is a single-date illustration. Many bonds have several possible call dates and prices, and their actual yield to worst can be lower than the result shown here. A valid modeled call date must occur before maturity and span at least one full coupon period. The cash-flow schedule, duration, modified duration, and convexity remain based on the maturity path even when a call scenario is enabled.
Duration and interest rate risk
Macaulay duration is the weighted-average time to receive the bond's cash flows, measured in years. Modified duration is Macaulay duration divided by (1 + y/n) and directly estimates the price sensitivity:
ΔPrice% ≈ −Modified Duration × ΔYield%
Convexity improves this approximation for large yield changes. A higher convexity means the bond price falls less (or rises more) than duration alone predicts.
Discount vs. premium bonds
When the YTM is above the coupon rate, the bond trades at a discount (price < face value). When YTM is below the coupon rate, it trades at a premium. At maturity the price always converges to face value, meaning discount bond holders earn a capital gain and premium bond holders take a capital loss (offset by the higher coupons they received).
Yield types glossary
| Yield type | Definition |
|---|---|
| Current yield | Annual coupon ÷ current market price. Ignores capital gain/loss at maturity. |
| Yield to maturity (YTM) | Total annualized return if held to maturity and coupons are reinvested at the same rate. |
| Yield to call (YTC) | Annualized yield calculated from coupons through one selected call date and the call price as redemption. This calculator rounds to whole coupon periods. |
| Yield to worst (YTW) | Here, the lower of maturity YTM and the single modeled YTC. Real bonds may have other call dates or prices that produce a lower yield. |
Bond laddering
A bond ladder is a portfolio of bonds with staggered maturity dates - e.g., one bond maturing each year for five years. As each bond matures, proceeds are reinvested at the long end of the ladder. This strategy reduces reinvestment risk (you are never fully exposed to a single interest rate environment) and provides periodic liquidity. The same principle applies to CDs - see the CD Ladder Calculator for an interactive example.
Federal, corporate, and municipal bonds
Bond type affects after-tax yield significantly:
- US Treasury bonds: exempt from state and local income taxes; subject to federal income tax. Considered the lowest credit risk available in USD.
- Corporate bonds: fully taxable at all levels. Higher coupon rates compensate for credit risk and full tax exposure.
- Municipal bonds ("munis"): interest is often exempt from federal income tax, while state treatment depends on the bond and your circumstances. Enable Tax-exempt income (muni) and enter a federal marginal rate to see the federal-only tax-equivalent yield (TEY) = tax-exempt YTM ÷ (1 − federal rate). The calculator never infers your bracket.
This simplified comparison does not account for state taxes, the alternative minimum tax (AMT), or private-activity bond rules. Those details can change the after-tax result. Use the Tax Bracket Estimator if you want help estimating a bracket, and consult a tax professional about your situation.
Frequently asked questions
What is yield-to-maturity (YTM)?
Yield-to-maturity is the total annualized return you would earn if you bought the bond at the current price and held it until maturity, assuming all coupon payments are reinvested at the same rate. It is the discount rate that makes the present value of all future cash flows equal to the current price.
What is the difference between current yield and YTM?
Current yield is simply the annual coupon divided by the current price - it ignores the gain or loss at maturity. YTM accounts for both the coupon income and the capital gain (or loss) from buying below (or above) face value. For a discount bond, YTM > current yield > coupon rate.
What is Macaulay duration?
Macaulay duration is the weighted-average time (in years) to receive all of a bond's cash flows, with weights based on the present value of each payment. It measures how long it takes, on average, to get your money back. Higher duration means more sensitivity to interest rate changes.
What is modified duration?
Modified duration = Macaulay duration ÷ (1 + YTM/frequency). It measures the percentage price change for a 1% (100 bps) change in yield. For example, a modified duration of 7 means the bond price will fall approximately 7% if yields rise by 1%.
Why does a bond trade at a discount or premium?
A bond trades at a discount (below face value) when current market yields are higher than its coupon rate. It trades at a premium when market yields are lower. At maturity, the price always converges to face value regardless of where it traded during its life.
How does the optional yield-to-call calculation work?
When Callable bond is enabled, the calculator discounts coupons through one selected call date and uses the entered call price as the final redemption amount. The call date is rounded to whole coupon periods and must be before maturity. Real bonds can have several call dates and prices; this tool models only one.
What does yield-to-worst (YTW) mean here?
With a valid single call date enabled, this calculator reports the lower of its maturity YTM and its modeled single-date YTC. A real bond may have other call dates, prices, or terms that produce a lower yield, so this is not a full call-schedule YTW analysis.
How is the municipal bond tax-equivalent yield estimated?
For the optional federal-only estimate, the calculator divides tax-exempt YTM by (1 − your entered federal marginal rate). You must enter the rate yourself. State tax rules, AMT, and private-activity bond treatment are not modeled, so this is an educational comparison rather than tax advice.
Related tools
- Tax Bracket EstimatorTax-equivalent yield for munis uses your federal marginal rate.
- Present ValueBond price is the present value of coupon and principal cash flows.
- CAGR CalculatorCompare YTM against an equity CAGR on a similar holding period.
- Investment Fee CalculatorBond-fund expense ratios come straight out of yield.