What is this bond’s price or yield?
Enter the face value, the coupon, the dates and a yield to get the price, or switch to enter a price and get the yield to maturity.
- Price (clean)
- $925.61
A 5% bond maturing September 30, 2036 is priced at $925.61 for a yield to maturity of 6%.
- Price per $100 of face value
- 92.5613
- Full (dirty) price
- $925.61
- Accrued interest
- $0.00
- Current yield
- 5.4018%
- Macaulay duration (years)
- 7.895
- Modified duration
- 7.665
- Coupon payment
- $25.00
- Coupons left
- 20
- Next coupon date
- March 30, 2027
Answer for the example date Wednesday, September 30, 2026. It changes to today's date when the page loads.
Price (clean): $925.61. A 5% bond maturing September 30, 2036 is priced at $925.61 for a yield to maturity of 6%.
Price at other yields
The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use
How to calculate
Computes a fixed-coupon bond’s price from its yield to maturity, or its yield from its price, on any settlement date, with accrued interest by day count, current yield and duration.
Example with the default inputs (Find the Price, Face value $1,000.00, Coupon rate (yearly) 5%, Coupons a year Twice a year, Yield to maturity 6%, Settlement date September 30, 2026, Maturity date September 30, 2036, Day count 30/360 (US bond basis): corporate and municipal bonds) on the example date Wednesday, September 30, 2026: A 5% bond maturing September 30, 2036 is priced at $925.61 for a yield to maturity of 6%.
Method: Full price = Σ C ÷ (1 + y ÷ f)^(w + k) + F ÷ (1 + y ÷ f)^(w + N − 1), k = 0 … N − 1; accrued = C × (1 − w); clean price = full price − accrued. C = F × coupon ÷ f; w is the part of a coupon period from settlement to the next coupon, by the day count.
- Coupons are fixed and paid on schedule, and the face value is repaid at maturity; the bond is not called early.
- The yield is compounded as often as the coupons are paid, and the same compound discounting is used when one coupon is left.
- Coupon dates are not moved for weekends or holidays.
- This is an estimate, not investment advice.
Worked examples
Each example is checked against the calculator on every build.
- Find the Price, Face value $100.00, Coupon rate (yearly) 5.75%, Coupons a year Twice a year, Yield to maturity 6.5%, Settlement date 2008-02-15, Maturity date 2017-11-15, Day count 30/360 (US bond basis): corporate and municipal bonds gives Price (clean) $94.63, Accrued interest $1.44, Coupons left 20, Next coupon date 2008-05-15.Source: Microsoft Excel PRICE function example: $94.63 (https://support.microsoft.com/en-us/office/price-function-3ea9deac-8dfa-436f-a7c8-17ea02c21b0a)
- Find the Yield to maturity, Face value $100.00, Coupon rate (yearly) 5.75%, Coupons a year Twice a year, Price (clean) $95.04, Settlement date 2008-02-15, Maturity date 2016-11-15, Day count 30/360 (US bond basis): corporate and municipal bonds gives Yield to maturity 6.5%.Source: Microsoft Excel YIELD function example: 6.5% (https://support.microsoft.com/en-us/office/yield-function-f5f5ca43-c4bd-434f-8bd2-ed3c9727a4fe)
- Find the Price, Face value $100.00, Coupon rate (yearly) 8%, Coupons a year Twice a year, Yield to maturity 9%, Settlement date 2018-07-01, Maturity date 2048-01-01, Day count Actual/Actual (ICMA): Treasury bonds gives Macaulay duration (years) 10.919145.Source: Microsoft Excel DURATION function example: 10.9191453 (https://support.microsoft.com/en-us/office/duration-function-b254ea57-eadc-4602-a86a-c8e369334038)
- Find the Price, Face value $100.00, Coupon rate (yearly) 8%, Coupons a year Twice a year, Yield to maturity 9%, Settlement date 2008-01-01, Maturity date 2016-01-01, Day count Actual/Actual (ICMA): Treasury bonds gives Modified duration 5.73567, Accrued interest $0.00.Source: Microsoft Excel MDURATION function example: 5.736 (https://support.microsoft.com/en-us/office/mduration-function-b3786a69-4f20-469a-94ad-33e5b90a763c)
- Find the Price, Face value $1,000.00, Coupon rate (yearly) 6%, Coupons a year Twice a year, Yield to maturity 6%, Settlement date 2026-01-15, Maturity date 2036-01-15, Day count Actual/Actual (ICMA): Treasury bonds gives Price (clean) $1,000.00, Price per $100 of face value 100, Current yield 6%, Accrued interest $0.00.Source: The Microsoft Excel PRICE formula with the yield equal to the coupon on a coupon date (https://support.microsoft.com/en-us/office/price-function-3ea9deac-8dfa-436f-a7c8-17ea02c21b0a)
How the bond price and yield are worked out
Inputs. Face value F, yearly coupon rate (percent), coupons a year f (1, 2, 4 or 12), settlement date, maturity date, day count, and either the yield to maturity y (percent a year) or the clean price for the whole face value. Find the picks which to work out.
Coupon dates. The coupon dates run back from the maturity date in steps of 12 ÷ f months: maturity, maturity minus 12 ÷ f months, and so on. Each date is worked out from the maturity date, and a day past the end of a shorter month becomes that month's last day (a maturity on August 31 gives February 28 or 29). Dates are not moved for weekends or holidays. The previous coupon date is the latest one on or before settlement, and the next coupon date the one after it. Coupons left, N, counts the coupon dates after settlement up to and including maturity. The settlement date must be before the maturity date, and at most 100 years before it.
Part of the period passed, a.
- Actual/Actual (ICMA): days from the previous coupon date to settlement ÷ days from the previous to the next coupon date.
- 30/360 (US bond basis, ISDA 4.16(f)): 30/360 days from the previous coupon date to settlement ÷ (360 ÷ f). 30/360 days = 360 × (Y₂ − Y₁) + 30 × (M₂ − M₁) + (D₂ − D₁), where a D₁ of 31 becomes 30, and a D₂ of 31 becomes 30 when D₁ is 30 or 31. There is no end-of-February rule.
- 30E/360 (Eurobond basis, ISDA 4.16(g)): the same, but any 31st becomes 30.
The part left to the next coupon is w = 1 − a.
Price. The coupon each period is C = F × coupon rate ÷ 100 ÷ f. With v = 1 ÷ (1 + y ÷ 100 ÷ f):
Full price = Σ C × v^(w + k) for k = 0 … N − 1, plus F × v^(w + N − 1)
Accrued interest = C × a. Clean price = full price − accrued interest. The same compound discounting is used when only one coupon is left (Excel's PRICE uses simple interest in that last period, so it can differ a little there).
Yield from a price. The clean price falls as the yield rises, so there is at most one yield for a price. The calculator bisects between −50% and 100% until the yield is found to about 14 significant digits. A price above the price at −50% or below the price at 100% has no answer. One case has no answer at any price: with one coupon left and a = 1 (w = 0, for example 30/360 settlement the day before a month-end maturity), the clean price is F at every yield, so a price gives no yield.
Other results.
- Price per $100 of face value = clean price ÷ F × 100.
- Current yield = C × f ÷ clean price × 100, when the clean price is above 0.
- Macaulay duration (years) = Σ ((w + k) ÷ f) × PV_k ÷ full price, where PV_k is each cash flow (the coupon, plus F at maturity) times v^(w + k).
- Modified duration = Macaulay duration ÷ (1 + y ÷ 100 ÷ f).
- Coupon payment = C.
Limits. Face value above $0 and at most $1 billion; coupon rate 0% to 100%; yield −50% to 100%; clean price above $0 and at most $10 billion. A result that is not a finite number (for example with a face value too small to count) is no answer.
Display. Money to the cent, rounded half up; the yield, the current yield, the price per $100 and the durations to 4 decimals. The bond is worked out in 64-bit floating point, so a value that is exactly a half in its last shown decimal can land just below it and show rounded down (a price per $100 of 101.76045 can show as 101.7604).
Chart. The price at yields from 5 points below to 5 points above the yield (within −49% to 100%), with the bond's own yield marked. The curve bends (convexity): the price rises more when the yield falls than it drops when the yield rises by the same amount.
Assumptions
- Coupons are fixed and paid on schedule, and the face value is repaid at maturity. Calls, sinking funds and default are not modelled.
- The yield is compounded as often as the coupons are paid.
- Every price and yield is typed; nothing is looked up. This is an estimate, not investment advice.
Worked examples by hand
Excel's PRICE example. F = 100, 5.75% coupon, twice a year, yield 6.5%, settled February 15, 2008, maturing November 15, 2017, 30/360. The coupon dates fall on May 15 and November 15. Previous coupon November 15, 2007; next May 15, 2008; 20 coupons left. 30/360 days from November 15 to February 15 = 360 − 270 = 90, so a = 90 ÷ 180 = 0.5 and w = 0.5. C = 2.875. v = 1 ÷ 1.0325. The coupons are worth Σ 2.875 × v^(0.5 + k) = 42.4744; the face value 100 × v^19.5 = 53.5974. Full price = 96.0719. Accrued interest = 2.875 × 0.5 = 1.4375. Clean price = 94.6344, as Excel gives ($94.63). Current yield = 5.75 ÷ 94.6344 = 6.0760%.
Excel's YIELD example. The same bond maturing November 15, 2016 at a clean price of 95.04287: the yield that gives this price is 6.5000% (6.5000007%, because Excel's price is rounded to 7 digits).
Excel's DURATION and MDURATION examples. 8% coupon, twice a year, yield 9%, Actual/Actual. Settled July 1, 2018 on a coupon date (a = 0, w = 1) and maturing January 1, 2048: Macaulay duration = 10.9191 years. Settled January 1, 2008 and maturing January 1, 2016: Macaulay duration 5.9938, modified duration = 5.9938 ÷ 1.045 = 5.7357.
At par. A $1,000, 6% bond paying twice a year, with a 6% yield, on a coupon date: v = 1 ÷ 1.03 and each $30 coupon and the $1,000 are discounted at exactly the coupon rate, so the price is $1,000.00, 100 per $100, with a current yield of 6% and no accrued interest.
Other questions people ask
How is a bond’s price worked out?
A bond’s price is the present value of its coupons and its face value, discounted at the yield to maturity. A 10-year $1,000 bond paying 5% twice a year ($25 each time) is worth $925.61 on a coupon date when the yield is 6%. When the yield is higher than the coupon, the price is below the face value; when it is lower, the price is above.
What is the yield to maturity?
It is the single yearly rate, compounded as often as the coupons are paid, at which the bond’s coupons and face value are worth exactly its price. It assumes you hold the bond to maturity and every payment arrives on time. The calculator finds it by trying yields until the price matches.
What is the difference between the clean and the full price?
Bonds are quoted at the clean price. Between coupon dates the seller has earned part of the next coupon, the accrued interest, and the buyer pays it on top: the full (dirty) price is the clean price plus the accrued interest. On a coupon date the two are equal.
Which day count should I use?
Use 30/360 for U.S. corporate, agency and municipal bonds, Actual/Actual for U.S. Treasury notes and bonds, and 30E/360 for many euro bonds. The day count decides how much of the current coupon has accrued: with 30/360 every month counts as 30 days, with Actual/Actual the real days count.
What is the current yield?
The current yield is the yearly coupon divided by the clean price. A 5.75% coupon bond at 94.634 has a current yield of 6.0760%. Unlike the yield to maturity, it ignores the gain or loss from buying below or above the face value.
What is duration?
Macaulay duration is the average time until the bond’s cash flows arrive, weighted by their present value, in years. Modified duration is Macaulay duration ÷ (1 + yield ÷ coupons a year) and says roughly how many percent the price moves when the yield moves by 1 point: with a modified duration of 7.18, a 1 point rise in yield lowers the price by about 7.18%.
Does the calculator look up bond prices?
No. You type the price or the yield, so nothing is fetched and the answer never changes on its own. Take them from your broker or TreasuryDirect.