Bond Yield (YTM) & Price Calculator
Yield, price, accrued interest and duration for any bond or treasury bill.
Cash flows
How this was calculated
Results are estimates for general information and planning, not financial advice. Banks and institutions may calculate differently (rounding, fees, rate changes). Confirm figures with your lender or a qualified adviser before deciding.
About the Bond Yield (YTM) & Price Calculator
A bond’s price and its yield are two views of the same thing: the yield to maturity is the one rate that discounts every coupon and the repayment to the price you pay. This calculator works either way — the yield to maturity, yield to call and current yield from a price, or the price from a yield — for coupons paid once, twice, four or twelve times a year, with the day counts bond markets use: 30/360, 30E/360, Actual/365, Actual/360 and Actual/Actual.
Between coupon dates it splits the price into the clean price that is quoted and the accrued interest the buyer pays the seller, and it adds Macaulay and modified duration, convexity and PV01, with a coupon-by-coupon schedule. A zero-coupon and treasury-bill mode gives the discount yield, the money-market yield and the yield by the formula of the Reserve Bank of India, (100 − P) ÷ P × 365 ÷ D.
How to use it
- Choose Coupon bond or Zero-coupon / T-bill, and whether to find the yield from a price or the price from a yield.
- For a coupon bond, enter the coupon rate and how often it is paid, then either the settlement and maturity dates (with the bond’s day count) or simply the years to maturity.
- Enter the price per 100 of face value — and say whether it is the clean price (as quoted) or the dirty price (with accrued interest) — or the yield in % a year.
- Optionally add a call date and price for the yield to call, and the face value you hold to see the amount you pay.
- Read the yields, the prices, the duration and the cash-flow schedule; copy the summary or download the schedule as CSV.
Examples
Settlement 15 Feb 2008, maturity 15 Nov 2017, 5.75% coupon twice a year, yield 6.50%, 30/360
Clean price 94.634362 · accrued interest 1.4375 (90 of 180 days) · dirty price 96.071862
An 8.83% bond with coupons on 25 May and 25 Nov, maturing 25 Nov 2023; settlement 30 Jan 2014, clean price 100.50, 30/360, face value 5 crore
65 days since the last coupon · accrued interest 1.594306 · dirty price 102.094306 · yield 8.7497% · you pay ₹5,10,47,152.78
This is the 8.83% GS 2023 example in RBI’s G-Sec primer, which rounds the accrued interest to 1.5943 and so gets ₹5,10,47,150.
A 2-year bond, 10% coupon twice a year, yield 9%
Price 101.79 · Macaulay duration 1.86 years · modified duration 1.78 · PV01 0.018 per 100
91 days to maturity, price 98.20
Yield on a 365-day basis 7.3521% · discount yield 7.1209% · effective annual yield 7.5575%
Common uses
- Work out the yield of a bond quoted at a price, before you buy.
- Price a bond at the yield of a similar one, or check a broker’s quote.
- Find the accrued interest and the amount you will pay on settlement.
- Compare the interest-rate risk of bonds by their duration and PV01.
- Convert a T-bill price into its yield, or a yield into the price to bid.
The formulas
With f coupons a year, a coupon C = 100 × coupon rate ÷ f per period, N coupons left, a redemption value R and a yield y:
- Dirty price = Σ C ÷ (1 + y/f)^(k − 1 + w) + R ÷ (1 + y/f)^(N − 1 + w), where w is the part of the current coupon period still to run. In the final coupon period the price is (R + C) ÷ (1 + w × y/f), with simple interest, as spreadsheet PRICE and YIELD functions do.
- Accrued interest = C × (days since the last coupon ÷ days in the coupon period); clean price = dirty price − accrued interest.
- Current yield = yearly coupon ÷ clean price; effective annual yield = (1 + y/f)^f − 1.
- Macaulay duration = the present-value-weighted average time of the cash flows; modified duration = Macaulay ÷ (1 + y/f); PV01 = modified duration × price × 0.0001.
The yield to maturity has no closed formula: the calculator solves for it with Newton’s method, kept inside a bracket and backed by bisection. These are the standard bond-maths definitions (Fabozzi, Fixed Income Mathematics).
Day counts
The day count decides how many days of interest have accrued and how long the coupon period is (ISDA 2006 Definitions, section 4.16):
- 30/360 (bond basis): every month counts as 30 days; a 31st counts as the 30th (the end date only when the start is the 30th or 31st). Common for US corporate bonds.
- 30E/360 (Eurobond basis): every 31st counts as the 30th. The RBI’s G-Sec primer says Indian government bonds use 30/360 and points to the European variant (spreadsheet basis 4).
- Actual/Actual (ICMA): actual days over the actual days of the coupon period — US Treasuries and UK gilts.
- Actual/365 (Fixed) and Actual/360: actual days over a 365- or 360-day year, mostly in money markets.
The US variant of 30/360 has an extra rule for the end of February; the calculator follows ISDA’s bond basis, so results for dates at the end of February can differ from a spreadsheet’s basis 0 by a day.
Clean and dirty prices
Bonds are quoted at the clean price. Between coupon dates the buyer also pays the seller the interest earned since the last coupon, so the money that changes hands is the dirty price (clean + accrued interest). On a coupon date the two are equal. The accrued interest is counted up to the settlement date, the day cash and bond change hands — usually one or a few business days after the trade.
Treasury bills and zero-coupon bonds
A T-bill pays no coupon: it is bought below 100 and repaid at 100. RBI’s primer gives its yield as (100 − P) ÷ P × 365 ÷ D: a 91-day bill at 98.20 yields 7.3521%. The discount yield, (100 − P) ÷ 100 × 360 ÷ D, measures the discount against the face value instead of the price, so it is always lower; the money-market yield uses the price and 360 days. For a long zero-coupon bond, compare the effective annual or half-yearly compounded yield with coupon bonds.
Limitations
- Coupons are regular: a bond with an odd (long or short) first or last coupon period, a floating or step-up coupon, inflation indexation or amortisation is not covered.
- The yield to call uses one call date and price; for bonds with several call dates, try each one — the lowest yield is the yield to worst.
- Settlement dates and holidays are not worked out for you: enter the settlement date of your trade.
- Taxes, fees and the reinvestment of coupons at a different rate are not included: the yield to maturity assumes every coupon earns the same yield.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
What is the difference between yield to maturity and current yield?
The current yield is only the yearly coupon divided by the clean price: 8.24 ÷ 103 = 8.00%. The yield to maturity also counts the gain or loss to the repayment at 100 and the timing of every payment, so a bond bought above 100 has a yield to maturity below its current yield.
Should I enter the clean or the dirty price?
Enter what you have and choose which it is. Bond quotes are usually clean prices; what you pay (before charges) is the dirty price × the face value ÷ 100. The yield is the same either way once the accrued interest is accounted for.
Why does the yield to maturity use the coupon frequency?
By market convention the yield is quoted as a yearly rate compounded as often as the coupon is paid — twice a year for most government bonds — so it can be compared with the coupon rate. The effective annual yield shows the same yield compounded once a year.
What does a modified duration of 6.4 mean?
The price falls by about 6.4% if the yield rises by 1 percentage point, and rises by about as much if the yield falls. Convexity makes the rise a little larger than the fall; for small changes, PV01 gives the price change for 0.01%.
How is a T-bill’s yield calculated in India?
By RBI’s formula: yield = (100 − price) ÷ price × 365 ÷ days to maturity × 100. A 91-day bill at 98.20 yields 7.3521%; the same bill trading at 99 with 50 days left yields 7.3737%.
What is the yield to worst?
The lowest yield you can get if the issuer does what is worst for you: for a callable bond, the lower of the yield to maturity and the yield to call.