A bond's price from coupon, yield and maturity, with duration.
Empty uses $1,000.
Example Result
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The calculated result will appear here after you press Calculate.
Estimates for planning only; not financial, tax or investment advice. See our Disclaimer.
A bond's price is what its future payments are worth today, at the yield buyers now demand. Enter the par value, coupon, yield and years to maturity, and pick how often it pays. The calculator gives the price in dollars and as a percent of par, with duration. Most US bonds pay twice a year, so that is the default.
Choose how often the bond pays. Check its terms, since most US bonds pay twice a year.
Enter the par value and the annual coupon rate.
Enter the market yield and the years to maturity, then press Calculate.
By O.E. — Partner, chairman of the board and CEO of a metal products manufacturer for 21 years; the company exports to 45 countries.
Drafted with AI assistance; calculations checked against primary sources and tested with the site's own code. About FlowUtil
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A plain bond pays a fixed coupon, then the par value at maturity. Each payment is discounted at the yield:
Price = Σ C ÷ (1 + y/f)^t + Par ÷ (1 + y/f)^n
C is the coupon per period, y the annual yield, f the payments per year, and n the number of periods. This is the same time value of money idea behind any present value. The NPV calculator does the same sum for uneven flows.
Par is $1,000, with 10 years to maturity, paying twice a year.
The bond pays more than new bonds do, so buyers pay a premium. That premium fades to zero by maturity. With annual payments, the price would be $1,081.11. The difference is small, but only one of them matches the actual bond.
Par is $1,000, with 5 years to maturity, paying twice a year.
This bond pays less than the market, so it sells at a discount. The buyer's return comes partly from the gain to par at maturity. To go the other way, from price to yield, use the bond yield calculator.
Coupons are fixed, so when market yields rise, the price has to fall until the bond pays the new yield. On the 5%, 10-year bond with annual coupons:
| Market yield | Price | Change from 4% |
|---|---|---|
| 3% | $1,170.60 | +8.3% |
| 4% | $1,081.11 | n/a |
| 5% | $1,000.00 | −7.5% |
Modified duration estimates this move. At 4% it is 7.88 years, so a 1 point rise suggests about −7.9%. The real fall is 7.5%, and the real gain from a fall in yield is larger, at 8.3%. That curve is called convexity. Duration works well for small moves and less well for large ones. Longer maturities and lower coupons mean more interest rate risk.
Macaulay duration is the weighted average time to get your money back, in years. Modified duration turns that into a price sensitivity. A zero-coupon bond has no coupons, so its Macaulay duration equals its maturity: a 10-year zero at 5% costs $613.91 and has a duration of 10 years.
Bonds are quoted without the interest built up since the last coupon. The buyer pays that accrued interest to the seller. On the 5% bond, 90 days into a 180-day period, accrued interest is $25 × 90 ÷ 180 = $12.50. So you would pay the quoted price plus $12.50.
The calculator assumes every payment arrives on time, a single yield for all periods, and no call feature. A callable bond may be repaid early, so its yield to maturity can overstate your return. Credit risk is in the yield you enter, not the formula. Taxes and dealer markups are not included. This is an educational estimate, not investment advice. For growth of reinvested coupons, see the compound interest calculator.