Bond Calculator
Price a bond from its yield, or find yield to maturity from a price — with current yield, total coupon income, duration and the full cash-flow table.
Bond Calculator: with the default inputs, bond price is $925.61.
In price mode the market yield is the input; in yield mode the market price is.
What the issuer repays at maturity. US corporate and Treasury bonds are quoted per $1,000.
The annual rate printed on the bond, as a percentage of face value. Enter 0 for a zero-coupon bond.
Used in price mode. The annual yield comparable bonds are offering today.
Used in yield mode. The clean price you'd pay, per bond.
Present value of every remaining coupon plus the face value at maturity.
- Yield to maturity
- 6%Annualised return if you hold to maturity and reinvest coupons at the same yield.
- Current yield
- 5.402%Annual coupon income ÷ price. Ignores the pull to par.
- Premium / (discount) to par
- -$74.39Price minus face value. Positive means the bond trades above par.
- Each coupon payment
- $25.00
- Total coupon income to maturity
- $500
- Total cash returned
- $1,500All coupons plus the face value repaid at maturity.
- Position value
- $926Price × number of bonds.
- Macaulay duration
- 7.89Weighted average time to the bond's cash flows, in years.
- Modified duration
- 7.67Approximate % price change for a 1 percentage-point move in yield.
Assumptions
- Clean price, settled on a coupon date: no accrued interest and no day-count fraction between coupons.
- Coupons are level and certain; no call, put, sinking fund or default risk is modelled.
- Yield to maturity assumes every coupon is reinvested at the yield to maturity itself.
- Years to maturity is rounded to a whole number of coupon periods.
- Modified duration is the first-order price sensitivity only — it ignores convexity, so it overstates losses and understates gains on large yield moves.
| Period | Years out | Cash flow | Present value |
|---|---|---|---|
| 1 | 0.5 | $25.00 | $24.27 |
| 2 | 1 | $25.00 | $23.56 |
| 3 | 1.5 | $25.00 | $22.88 |
| 4 | 2 | $25.00 | $22.21 |
| 5 | 2.5 | $25.00 | $21.57 |
| 6 | 3 | $25.00 | $20.94 |
| 7 | 3.5 | $25.00 | $20.33 |
| 8 | 4 | $25.00 | $19.74 |
| 9 | 4.5 | $25.00 | $19.16 |
| 10 | 5 | $25.00 | $18.60 |
| 11 | 5.5 | $25.00 | $18.06 |
| 12 | 6 | $25.00 | $17.53 |
Coupons are paid twice a year; the last period also repays the $1,000 face value.
How this is worked out
The formula
Price = C × [1 − (1 + y)⁻ⁿ] ÷ y + F × (1 + y)⁻ⁿ C = coupon per period = face value × coupon rate ÷ periods per year y = yield per period = annual yield ÷ periods per year n = number of periods remaining = years × periods per year F = face (par) value Current yield = annual coupon ÷ price Yield to maturity = the y that makes the equation above equal the market price (solved numerically), annualised Macaulay duration = Σ [ t × PV(cash flow at t) ] ÷ price, in periods, then ÷ periods per year Modified duration = Macaulay duration ÷ (1 + y)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- What do you want to find?
- In price mode the market yield is the input; in yield mode the market price is.Price — I know the yield I need · Yield to maturity — I know the price
- Face (par) value
- What the issuer repays at maturity. US corporate and Treasury bonds are quoted per $1,000.in dollars · 0 or more · defaults to 1000
- Coupon rate
- The annual rate printed on the bond, as a percentage of face value. Enter 0 for a zero-coupon bond.a percentage · from 0 to 100 · defaults to 5
- Years to maturity
- A number.from 0 to 100 · defaults to 10
- Coupons paid
- Choose one of 4 options.Once a year · Twice a year (US standard) · Quarterly · Monthly
- Market yield (required return)
- Used in price mode. The annual yield comparable bonds are offering today.a percentage · from 0 to 100 · defaults to 6
- Market price
- Used in yield mode. The clean price you'd pay, per bond.in dollars · 0.01 or more · defaults to 926.4
- Number of bonds(under More options)
- Scales the position value and coupon income; per-bond figures are unaffected.from 1 to 1000000 · whole numbers only · defaults to 1
What you get back
- Bond pricemain answer
- Present value of every remaining coupon plus the face value at maturity.
- Yield to maturity
- Annualised return if you hold to maturity and reinvest coupons at the same yield.
- Current yield
- Annual coupon income ÷ price. Ignores the pull to par.
- Premium / (discount) to par
- Price minus face value. Positive means the bond trades above par.
- Each coupon payment
- Total coupon income to maturity
- Total cash returned
- All coupons plus the face value repaid at maturity.
- Position value
- Price × number of bonds.
- Macaulay duration
- Weighted average time to the bond's cash flows, in years.
- Modified duration
- Approximate % price change for a 1 percentage-point move in yield.
What this assumes
- Clean price, settled on a coupon date: no accrued interest and no day-count fraction between coupons.
- Coupons are level and certain; no call, put, sinking fund or default risk is modelled.
- Yield to maturity assumes every coupon is reinvested at the yield to maturity itself.
- Years to maturity is rounded to a whole number of coupon periods.
- Modified duration is the first-order price sensitivity only — it ignores convexity, so it overstates losses and understates gains on large yield moves.
About this calculator
A bond is a fixed schedule of payments — a coupon every period and the face value at maturity — so its price is nothing more than the present value of that schedule at the yield the market currently demands. This calculator runs that valuation in both directions: give it a yield and it returns the price; give it a price and it solves for the yield to maturity.
Price and yield move in opposite directions
That is the single most important fact about bonds. If you hold a 5% coupon and rates rise to 6%, nobody will pay you par for a below-market coupon, so the price falls until the total return matches 6%. If rates fall to 4%, your bond trades at a premium. The premium / (discount) to par output shows which side you're on, and the size of the gap is roughly duration × the yield difference.
How to use it
Pick a mode. In price mode you enter the market yield and get the price — this is how you value a bond you already own, or check whether a quoted offer is fair. In yield mode you enter what the bond costs and get the yield to maturity, which is the number to compare across bonds. Set the coupon frequency to match the bond: US Treasuries and most US corporates pay twice a year, many European government bonds pay annually.
Reading the results
- Yield to maturity assumes you hold to maturity and reinvest every coupon at that same yield. Real reinvestment rates differ, so realised return rarely equals YTM exactly.
- Current yield is just coupon ÷ price. It ignores the capital gain or loss you book as the price pulls toward par, so it overstates the return on a premium bond and understates it on a discount bond.
- Macaulay duration is the weighted average time to your money, in years. Modified duration is the practical one: a modified duration of 7.5 means a 1 percentage-point rise in yield costs you roughly 7.5% of price. That approximation understates the gain and overstates the loss, because the price-yield relationship is convex.
Where this simplifies
The price here is a clean price on a coupon date — no accrued interest, no day-count fraction. Between coupon dates a buyer also pays accrued interest, and the invoice (dirty) price is higher; conventions differ (30/360 for US corporates, actual/actual for Treasuries). Callable bonds should be assessed on yield-to-worst rather than yield-to-maturity, since the issuer will redeem early exactly when it hurts you. Credit risk is not modelled at all: a yield to maturity is only achievable if the issuer actually pays. And nothing here accounts for tax — municipal bond interest is federally tax-exempt, Treasury interest is exempt from state tax, and corporate interest is fully taxable, which changes the ranking of otherwise-similar yields.
Frequently asked questions
▸What is yield to maturity?
The single discount rate that makes the present value of all remaining coupons plus the face value equal the bond's price. It's the internal rate of return of the bond, assuming you hold to maturity and can reinvest coupons at that same rate.
▸Why does my bond's price fall when interest rates rise?
Because the coupon is fixed. If new bonds pay 6% and yours pays 5%, buyers will only take yours at a discount deep enough to make the total return 6%. Longer maturities fall further, which is exactly what duration measures.
▸What's the difference between current yield and yield to maturity?
Current yield is annual coupon ÷ price and stops there. Yield to maturity also counts the pull to par — the gain on a discount bond or the loss on a premium bond — so it's the more complete measure.
▸Does this include accrued interest?
No. It prices the bond as if settlement falls on a coupon date, so it returns the clean price. Buying between coupon dates means also paying the seller the interest accrued since the last coupon.
▸How do I price a zero-coupon bond?
Set the coupon rate to 0. The price collapses to face value ÷ (1 + y)ⁿ, and Macaulay duration equals the time to maturity exactly, because there is only one cash flow.
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