Bond prices are quoted every second, but the number you see on a screen is not what you pay. Quotes are clean prices; at settlement you also pay the seller the interest that has accrued since the last coupon. This calculator prices a fixed-rate bond on an exact settlement date the way bond desks do, and adds the risk measures — duration and convexity — that tell you how much the price will move when interest rates change.
How to use the bond price calculator
- Enter the face value, the annual coupon rate and the market yield you want to price at.
- Choose the coupon frequency — semiannual for most US bonds.
- Enter the settlement date (the day cash changes hands) and the maturity date. Coupon dates are counted backward from maturity.
- Pick the day count: Actual/Actual for Treasuries, 30/360 for most corporate and municipal bonds.
- Read the clean price, accrued interest and dirty price, then the sensitivity table.
Bond pricing formulas
With coupon C per period, yield y, f coupons a year, N coupons left and w the fraction of a period until the next coupon:
Each cash flow CF is a coupon, plus the face value at maturity. tk is the time to each payment in years.
Worked example
A $1,000 bond pays a 5% coupon semiannually on May 15 and November 15 and matures on May 15, 2036. It settles on October 15, 2026 at a market yield of 6%, using Actual/Actual.
Coupon = $25 per half-year; 20 coupons remain; the last coupon was May 15, 2026
Days in the period = 184; days since the last coupon = 153 → w = 31 ÷ 184 = 0.168478
Dirty price = $948.64; accrued interest = 25 × 153 ÷ 184 = $20.79
Clean price = 948.64 − 20.79 = $927.86 (a quote of 92.786)
The bond’s modified duration is 7.261 and its convexity 65.56. If yields jumped to 8%, duration alone would predict a clean price near $790; adding convexity gives $802.53, very close to the true $801.75.
How price and yield interact
- Price and yield move in opposite directions. The sensitivity table shows prices for yields from two points below to two points above your input.
- Discount and premium. When the coupon rate is below the market yield, the bond prices below par; when it is above, it prices above par.
- Duration grows with maturity and shrinks with higher coupons, because more of the bond’s value arrives sooner.
- DV01 is the dollar change for a one-basis-point (0.01%) move in yield — the number traders use to size hedges.
To go the other way — from a price to a yield — use the bond yield calculator. The discounting here is the same idea as the present value of cash flows calculator, applied on a fixed coupon schedule.
Prices are estimates for education and planning, not investment advice. Real trades may involve odd first or last coupons, business-day adjustments and dealer markups that this calculator does not model.
Frequently asked questions
How is a bond's price calculated?
A bond's price is the present value of its remaining coupons and its face value, each discounted at the market yield for the time until it is paid. Between coupon dates, the time to each payment includes a fraction of a period, which is why exact settlement and maturity dates matter.
What is the difference between the clean and dirty price?
The dirty (full) price is what the buyer actually pays. It includes interest that has built up since the last coupon, which belongs to the seller. The clean price strips that accrued interest out, so it does not jump on coupon dates. Bond prices are quoted clean.
What does modified duration tell me?
Modified duration estimates the percentage change in a bond's price for a one-percentage-point change in yield. A modified duration of 7.26 means the price falls about 7.26% if yields rise by one point, and rises about the same if they fall. Longer maturities and lower coupons mean higher duration.
Why do I need convexity as well as duration?
Duration is a straight-line estimate, but the real price–yield relationship curves. Convexity measures that curve: it makes prices rise a little more than duration predicts when yields fall, and fall a little less when yields rise. For large yield moves, adding convexity makes the estimate much more accurate.
Which day count should I use?
US Treasury notes and bonds use Actual/Actual, counting the real days in each coupon period. Most US corporate and municipal bonds use 30/360, which treats every month as 30 days. The choice changes accrued interest by a few cents to a few dollars per bond.