How to use the bond calculator
- Choose whether to find the price from a yield or the yield from a price.
- Enter the bond's face (par) value, usually $1,000, its annual coupon rate and how many coupons it pays each year (most US bonds pay twice a year).
- Enter the time to maturity, either as years or as a settlement date and maturity date. Use dates when you are buying between coupon dates, so accrued interest is counted.
- Enter the yield to maturity (to find the price) or the quoted clean price (to find the yield).
How bond prices are calculated
C is each coupon (face × coupon rate ÷ coupons a year), F is the face value, j is the yield per period (annual yield ÷ coupons a year), n is the number of coupons left and w is the fraction of a coupon period until the next coupon. When you enter whole years, w is 1 and the formula becomes the familiar sum of an annuity and a lump sum. With dates, w is the actual days to the next coupon divided by the days in the coupon period. Yield to maturity has no direct formula, so the calculator finds the yield whose price matches the one you enter by repeated halving.
Current yield is the annual coupon divided by the clean price. Macaulay duration is the average time to each cash flow, weighted by its present value; modified duration (Macaulay ÷ (1 + j)) estimates the percentage change in price for a one-point change in yield.
Worked example
The defaults are a $1,000 bond with a 5% coupon paid twice a year, 10 years from maturity, priced at a 6% yield.
- Each coupon: $1,000 × 0.05 ÷ 2 = $25. Yield per period: 6% ÷ 2 = 3%. Coupons left: 20.
- Present value of the coupons: $25 × (1 − 1.03^−20) ÷ 0.03 = $25 × 14.877475 = $371.937.
- Present value of the face value: $1,000 ÷ 1.03^20 = $553.676.
- Price: $371.937 + $553.676 = $925.61, a discount of $74.39 to face.
The current yield is $50 ÷ $925.61 = 5.402%. The Macaulay duration is 7.89 years and the modified duration is 7.67, so a one-point rise in yield would cut the price by roughly 7.7%.
Turned around, a price of $950 implies a yield to maturity of 5.662%. Bought on January 15, 2027, a bond maturing May 15, 2036 has 19 coupons left and is 61 days into a 181-day coupon period; at a 6% yield its clean price is $929.25, plus $8.43 of accrued interest.
Premium, discount and par
| Coupon rate vs. yield | Price | Called |
|---|---|---|
| Coupon above the yield | Above face value | Premium bond |
| Coupon equal to the yield | Equal to face value | At par |
| Coupon below the yield | Below face value | Discount bond |
Bond prices move opposite to yields: when market yields rise above a bond's coupon, buyers pay less for it, so the coupon plus the gain to par at maturity matches the new yield. As maturity nears, every bond's price drifts toward par.
Frequently asked questions
What is the difference between clean and dirty price?
Bonds are quoted at the clean price, which leaves out interest that has built up since the last coupon. When you buy, you pay the clean price plus accrued interest, which is the dirty (or full) price, because the seller earned that part of the next coupon. On a coupon date the two are equal.
Is yield to maturity the return I will actually get?
Only if you hold the bond to maturity, it pays every coupon on time, and you reinvest each coupon at the same yield. If rates change, your reinvestment return changes too, and selling before maturity means selling at whatever the market price is then.
Why are yields quoted per half-year and doubled?
US bond yields follow the bond-equivalent convention: the yield per coupon period multiplied by the number of periods in a year. A 6% semiannual yield means 3% every six months, which compounds to an effective annual yield of 6.09%.
What does duration tell me?
Duration measures interest rate risk. A bond with a modified duration of 7.67 loses about 7.67% of its value if yields rise one percentage point, and gains about the same if they fall. Longer maturities and lower coupons mean higher duration.
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Results are estimates for educational purposes and are not financial, tax or legal advice. See our disclaimer.