Yield to maturity (YTM) is the annual rate of return a bond delivers if you buy it at today's price, keep it until it matures and receive every payment on schedule. Technically it is the one discount rate at which the present value of all remaining coupons plus the face value equals the price; FINRA defines it in exactly those terms. A bond priced below face value has a YTM above its coupon, and one priced above face value has a YTM below it. For the securities this page draws on, start at the US Treasuries hub.
How is yield to maturity calculated?
You find the rate y that makes the discounted value of every remaining payment equal to the bond's price, usually by trial and error or a spreadsheet.
C is the annual coupon per $100 of face value, n is the number of half-yearly payments left and y is the yield to maturity. Treasuries pay every six months, so the equation runs in half-years and y is quoted as twice the half-year rate. Treasury's auction rules, in Appendix B to 31 CFR Part 356, define the yield the same way: a nominal annual rate based on semiannual payments. With more than one payment left there is no algebraic answer. You guess a rate, compute the price, and adjust; a higher guess always produces a lower price, so the search narrows fast.
For a check by hand, a shortcut spreads the discount or premium evenly over the years left and divides the result by the average of price and face value:
It works well near 100 and drifts for deep discounts. It gives 4.894% for the 7-year note below, but 5.561% for the 30-year bond Treasury reopened on October 8, 2026 at 92.889131, whose true yield was 5.618%. Running the equation the other way, from yield to price, is the subject of why bond prices fall when rates rise.
What yield to maturity did the October 2026 7-year note offer?
Solving the equation at its auction price of 99.887964 gives 4.894%, the same high yield Treasury announced on October 29, 2026.
Worked example: Solving for the yield on the 7-year note auctioned October 29, 2026
The note (CUSIP 91282CRV5) pays a 4.875% coupon, $2.4375 per $100 every April 30 and October 31, and matures on October 31, 2033: 14 payments in all. It sold at 99.887964 per $100.
| Trial yield | Price from the equation |
|---|---|
| 4.875% | 100.0000 |
| 4.950% | 99.5608 |
| 4.900% | 99.8534 |
| 4.890% | 99.9120 |
| 4.894% | 99.8885 |
- At 4.875% the yield equals the coupon and the price is exactly 100, so the true yield must be higher.
- 4.950% overshoots, giving too low a price; 4.900% comes close at 99.8534.
- Interpolating between 4.890% and 4.900%: 4.890 + 0.010 × (99.9120 − 99.8880) ÷ (99.9120 − 99.8534) = 4.894%.
- On $10,000 of face value the note cost $9,988.80, plus $2.69 of accrued interest for October 31 to November 2.
Treasury's own conversion in Appendix B starts on the November 2 issue date instead of the October 31 dated date and discounts the 179 days to the first coupon at simple interest. That is why the simple 14-payment equation gives 99.8885 at 4.894% rather than the official 99.887964, a gap of about 6 cents on $10,000. Every winning bidder, competitive or not, received the same 4.894%; how Treasury auctions work explains how the high yield is found, and Treasury notes explained covers the payment calendar.
How is yield to maturity different from current yield and the coupon rate?
The coupon rate is income on face value, current yield is income on today's price, and YTM also counts the gain or loss back to face value.
| Measure | How it is calculated | 7-year note, October 29, 2026 | 30-year bond reopening, October 8, 2026 |
|---|---|---|---|
| Price per $100 | Set at auction | 99.887964 | 92.889131 |
| Coupon rate | Fixed when first issued | 4.875% | 5.125% |
| Current yield | Annual coupon ÷ price | 4.880% | 5.517% |
| Yield to maturity | Rate that equates price and all payments | 4.894% | 5.618% |
| Effective annual yield | (1 + YTM ÷ 2)^2 − 1 | 4.954% | 5.697% |
Below par the three measures rise in that order: the buyer collects the coupon, earns it on a smaller outlay and also gains the discount at maturity. Above par the order flips, with YTM under current yield and current yield under the coupon. TreasuryDirect states the rule in one table: a yield above the interest rate means a price below par, an equal yield means par, and a lower yield means a premium. The current yield and coupon rate entries define the other two measures in full.
The last row matters when a Treasury is set against a bank deposit. Treasury yields compound twice a year, so the note's 4.894% is worth 4.954% compounded once a year, the basis an APY uses; APY vs APR shows the conversion.
What does yield to maturity assume about reinvesting coupons?
The arithmetic assumes every coupon is reinvested at the YTM itself until maturity; reinvest at a different rate and your realized return moves toward that rate.
FINRA's wording is careful: YTM does not require reinvestment, but its calculation generally assumes it, and because rates keep moving, coupons are almost never reinvested at exactly the YTM. The example holds the 7-year note to maturity and changes only what its coupons earn.
Worked example: Reinvesting the 7-year note's coupons at three rates
Buy $10,000 of face value for $9,988.80, leaving aside the $2.69 of accrued interest that the first coupon repays. The note pays 14 coupons of $243.75, or $3,412.50 in all, plus $10,000 in October 2033.
| Rate earned on reinvested coupons | Interest on interest | Value in October 2033 | Realized annual return |
|---|---|---|---|
| 3.894% | $467.38 | $13,879.88 | 4.755% |
| 4.894%, the YTM | $599.66 | $14,012.16 | 4.894% |
| 5.894% | $737.37 | $14,149.87 | 5.037% |
- At the YTM, the $4,023.36 gain splits into $3,412.50 of coupons, $11.20 of discount repaid at maturity and $599.66 of interest on interest.
- Realized return = 2 × ((ending value ÷ $9,988.80)^(1 ÷ 14) − 1), the same semiannual convention as the YTM.
Reinvesting a full point lower trims the seven-year return by 0.14 point, and a point higher adds 0.14. The effect grows with maturity and coupon size, so it matters far more for a 30-year bond than for a 2-year note. A zero-coupon security has nothing to reinvest, so its YTM is earned exactly if it is held to maturity; Treasury STRIPS explained covers those. To test other reinvestment rates, use the compound interest calculator.
Where do you see yield to maturity quoted?
Treasury auction results, the daily par yield curve, broker bond quotes and fund fact sheets all report some form of yield to maturity.
- Auction results. Competitive bidders state the YTM they will accept, and the announced high yield is the YTM every winner gets at the auction price.
- The par yield curve. Treasury's daily curve shows par yields, the coupon a new note or bond would need to sell at exactly 100, which is also its YTM. The 10-year yield quoted in the news, 4.94% on October 30, 2026, is one of these; the Treasury yield curve page tracks them.
- Broker quotes. Buying at the ask price gives a slightly lower YTM than the bid side shows. Callable corporate and municipal bonds also list yield to call and yield to worst.
- Fund fact sheets. Bond funds often publish the average YTM of their holdings. It describes the portfolio on one date, not a return the fund will deliver, because a fund keeps trading and never matures.
- Treasury bills. Bills pay no coupon. Their investment rate, which Treasury calls the coupon equivalent, is the figure Treasury says to compare with a coupon security maturing on the same date; T-bill discount rate vs investment rate shows the conversion.
What do people get wrong about yield to maturity?
The biggest misreading is treating YTM as a promised return, when it holds only for a buyer who keeps the bond to maturity and reinvests at that rate.
- Selling early. A sale before maturity earns whatever the price is that day, not the YTM at purchase; selling Treasuries before maturity shows how that works.
- Leaving out taxes and costs. FINRA notes that YTM ignores taxes and brokerage costs. Treasury interest is taxed federally but not by states, as are T-bills taxable? explains.
- Comparing unlike conventions. A note's semiannual YTM, a bill's discount rate and a deposit's APY are three different conventions. Convert them to one basis before comparing.
- Reading a higher YTM as a better deal. Extra yield usually pays for something: more credit risk, a longer maturity or more price risk. On October 30, 2026 the 10-year Treasury yielded 4.94% against 4.56% for the 2-year, but its price moves about four times as much when yields change.
- Confusing the estimate with the result. YTM looks forward from the purchase price. Your total return can only be measured after you sell or the bond matures, from the cash you actually received.