Bond yield calculator
Enter a bond's terms and the price you would pay. This solves yield by root finding rather than approximating it, prices every date in the call schedule, and states the reinvestment assumption yield to maturity makes silently.
Worked example — Yield to worst on a premium callable corporate: 4.103%. 5.5% coupon, 2036-08-30 maturity, 104.500 clean price, calls at 102.000 and 100.000
Premium callable corporate: A premium bond trading above two call prices, the scenario that makes yield to worst diverge from yield to maturity.
Advanced: your reinvestment assumption 1
Yields are quoted with 2 compounding periods a year, the same convention as the coupon, so they line up with a broker quote. Everything is solved from the dirty price, because that is the money that changes hands.
Why the approximation is still everywhere
The formula (C + (F - P) / n) divided by the average of face and price predates cheap root finding, and it survives in calculators because it fits on one line. On this bond it is off by 1.4 basis points. On a long zero-coupon or deep discount bond it drifts much further.
What yield to maturity quietly assumes
At a reinvestment rate of 3.00%, interest earned on interest is 5.3% of everything the bond hands back. Yield to maturity treats that share as guaranteed at the quoted yield. It is not, and for a long high-coupon bond it is most of the answer.
Accrued interest is not optional
0 of 182 days of this coupon period belong to the seller, so the settlement amount is 104.500 rather than the quoted 104.500. Under 30/360 the same trade accrues 0.000 instead. The quote does not move, the cash does.
This tool computes from the terms you type. It does not read a price, a curve, or a call schedule from any venue, and it does not model an option value on the call.
Every way this bond can be redeemed
A callable bond gives the issuer the choice, and the issuer takes it when it suits the issuer. Yield to worst prices every redemption date in the schedule at the same purchase price and reports the lowest of them. On the premium callable corporate above, every call pays less than holding to maturity, which is what a premium bond above its call prices looks like.
| Redemption | Date | You receive | Years | Yield | Versus maturity |
|---|---|---|---|---|---|
| Held to maturity | 2036-08-30 | 100.000 | 10.00 | 4.925% | +0.0 bp |
| Called at 102.00, the worst case | 2028-08-30 | 102.000 | 2.00 | 4.103% | -82.2 bp |
| Called at 100.00 | 2031-08-30 | 100.000 | 5.00 | 4.485% | -43.9 bp |
What's the difference between yield to maturity, current yield, and yield to worst?
Four numbers on a bond quote all get called "the yield," and they answer different questions. Yield to maturity is the rate that makes every remaining cashflow, discounted at one rate, equal the price paid; it assumes every coupon is reinvested at that same rate until maturity. Current yield ignores that entirely and is just the coupon over the price. Yield to worst is the lowest yield across maturity and every call date, priced at the same purchase price, and it is the number a callable bond should be bought on.
| Measure | Value | Difference from yield to maturity | What it assumes |
|---|---|---|---|
| Yield to maturity, solved | 4.9247% | reference | Every coupon is reinvested at this same yield until maturity. |
| Textbook approximation | 4.9389% | +1.4 bp | Nothing defensible. It averages the price and the face and calls the result a yield. |
| Current yield | 5.2632% | +33.8 bp | That the pull to par never happens. It ignores the capital gain or loss entirely. |
| Yield to worst | 4.1032% | -82.2 bp | The issuer exercises whichever redemption is worst for the holder. |
Worked example: a premium callable corporate bond
A 5.5% coupon bond maturing 2036-08-30, bought today at a clean price of 104.500, callable at 102.000 in 2028-08-30 and at 100.000 in 2031-08-30, solves to a yield to maturity of 4.925%. But this bond trades above both call prices, so the issuer has every reason to call it early: the called at 102.00 on 2028-08-30 is the worst redemption for the holder, and it prices to 4.103%, 82 basis points below yield to maturity. That gap is why yield to worst, not yield to maturity, is the number to plan on for a premium callable bond.
Why is the price I pay different from the quoted price?
Bonds are quoted clean and settle dirty. Between coupon dates the buyer owes the seller the interest that has accrued since the last coupon, under a day-count convention that is a property of the security, not a preference. On the default bond, 0 of 182 days of the current coupon period belong to the seller, so the settlement amount is 104.500 rather than the quoted 104.500. Most free calculators ignore this and quote a price nobody actually pays.
What JMM thinks
Yield to maturity is a return you receive only if every coupon reinvests at that same yield until maturity, which almost never happens. Treat it as a pricing convention, not a forecast. Buy the yield to worst, sanity-check the realised yield under a reinvestment rate you would actually accept, and ignore the current yield entirely. Price and yield are inverted here by Newton's method on the analytic derivative, with bisection as a fallback, and the round trip holds to within 1e-10 in testing.
What this does not model: credit risk or default probability, so a solved yield is what you earn if every payment arrives; option-adjusted spread, so a call is priced as a date rather than as an option the issuer owns; taxes, fees, or sinking funds. For the tax side use the tax-equivalent yield calculator; for price sensitivity to a rate move use the duration and convexity calculator; for a security with no coupons use the Treasury bill yield calculator.
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Duration and convexity calculatorCalculatorYield says what the bond pays if nothing moves. Duration and convexity say what a rate move costs if it does.Open nextOther questions
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