๐ Bond Calculator
Bond Calculator โ Price, YTM & Coupon
Calculate bond price from yield, find yield to maturity from price, and see clean/dirty price, accrued interest, Macaulay duration, and full coupon payment schedule.
P = ฮฃ C/(1+r)แต + F/(1+r)แดบ
Bond Price
Dirty = Clean + Accrued Interest
Price Types
Current Yield = C / Price
Current Yield
๐ฐ Bond Price & YTM
๐ Clean & Dirty Price
โฑ๏ธ Macaulay Duration
๐
Coupon Schedule
Bond Calculator
Price ยท Yield to Maturity ยท Clean/Dirty Price ยท Duration
๐ฐ Bond Price
๐ Yield to Maturity
๐
Price with Dates
Bond Details
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yrs
days
Find Yield to Maturity
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$
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yrs
Bond Pricing with Settlement Date
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$0
Clean Price
0%
YTM
0%
Current Yield
$0
Coupon/Period
Clean Price ยท Dirty Price ยท Accrued Interest
$0
Clean Price (Quoted)
$0
Accrued Interest
$0
Dirty Price (Invoice)
Dirty Price = Clean Price + Accrued Interest. The dirty price is what you actually pay when buying between coupon dates.
Duration โ Interest Rate Sensitivity
Duration measures how much the bond price changes per 1% rate move.
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Macaulay (yrs)
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Modified (%)
๐ Bond Price vs Yield โ Sensitivity Curve
๐ Coupon Payment Schedule
| Period | Coupon Payment | Principal | Total Cash Flow | PV of Cash Flow | Cumulative PV |
|---|---|---|---|---|---|
| Enter bond details to see schedule | |||||
Bond Pricing Formula Explained
A bond's fair price equals the present value of all future cash flows: periodic coupon payments plus the face value at maturity. The formula is:
P = ฮฃ[C / (1+r)แต] + F / (1+r)แดบ
- P = Bond price
- C = Coupon payment per period (Face Value ร Annual Rate รท Frequency)
- r = Yield per period (Annual YTM รท Frequency)
- N = Total number of periods
- F = Face value (par value)
If the coupon rate equals the yield, the bond prices at par ($1,000). If the yield exceeds the coupon rate, the bond trades at a discount (below $1,000). If the coupon rate exceeds the yield, the bond trades at a premium (above $1,000).
Bond Pricing Examples
| Scenario | Face Value | Coupon | YTM | Term | Bond Price | Status |
|---|---|---|---|---|---|---|
| At Par | $1,000 | 5% | 5% | 10 yrs | $1,000.00 | At Par |
| At Discount | $1,000 | 5% | 7% | 10 yrs | $859.53 | Discount (โ14%) |
| At Premium | $1,000 | 7% | 5% | 10 yrs | $1,154.43 | Premium (+15.4%) |
| Zero-Coupon | $1,000 | 0% | 5% | 10 yrs | $613.91 | Deep Discount |
| Short-Term | $1,000 | 5% | 6% | 2 yrs | $981.57 | Discount (โ1.8%) |
Yield to Maturity (YTM) vs Other Yield Measures
| Yield Measure | Formula | Best Used For |
|---|---|---|
| Nominal Yield | Annual Coupon / Face Value | Quick reference โ equals the coupon rate |
| Current Yield | Annual Coupon / Market Price | Income relative to current price |
| Yield to Maturity | Discount rate = NPV of all cash flows to price | Total return if held to maturity |
| Yield to Call (YTC) | Same as YTM but to call date | Callable bonds โ if called early |
| Yield to Worst (YTW) | Lowest of YTM and all YTC values | Worst-case return on callable bonds |
Frequently Asked Questions
Bond price = PV of coupons + PV of face value. P = ฮฃ[C/(1+r)แต] + F/(1+r)แดบ. For a $1,000 bond with 5% semiannual coupons, 10 years, and 6% yield: C=$25, r=3%, N=20 periods. P = 25ร[1-(1.03)โปยฒโฐ]/0.03 + 1000/(1.03)ยฒโฐ = $371.53 + $553.68 = $925.61.
YTM is the total return expected on a bond held to maturity, assuming all coupons are reinvested at the same rate. It's the discount rate that makes the present value of all future cash flows equal to the current price. YTM is solved numerically (no closed-form solution) โ our calculator uses Newton-Raphson iteration to find the precise YTM.
When market interest rates rise, newly issued bonds offer higher yields. Existing bonds with lower coupon rates become less attractive in comparison. To make them competitive, their prices must fall until their yield (relative to price) matches the new market rate. This inverse relationship is fundamental to fixed income: price and yield always move in opposite directions.
Clean price is the quoted market price excluding accrued interest. Dirty price (invoice price) is what you actually pay โ clean price plus interest that has accrued since the last coupon date. If you buy a bond midway between coupon dates, you compensate the seller for the interest they earned. At the next coupon date, you receive the full coupon payment (which returns the accrued interest you paid).
Macaulay duration is the weighted average time to receive all cash flows, measured in years. Modified duration (= Macaulay duration / (1+YTM/n)) tells you the approximate percentage price change for a 1% change in yield. A modified duration of 7 means the bond price will change approximately 7% for each 1% change in yield. Longer duration = more price sensitivity = more interest rate risk.
Government bonds (US Treasuries, gilts) โ lowest default risk, lowest yield. Municipal bonds โ often tax-exempt, issued by state/local governments. Corporate bonds โ higher yield, higher credit risk, rated by agencies. Zero-coupon bonds โ no periodic payments, sold at deep discount. Inflation-protected bonds (TIPS) โ principal adjusts with inflation. Convertible bonds โ can be converted to stock. Each type has different risk/return characteristics.