Yield to maturity
The single yearly rate, compounded twice a year, at which a bond's remaining payments are worth exactly its price today.
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How it is computed here
Solved numerically from the bond's estimated full price (the price plus accrued interest) and its payment calendar: the rate y such that the payments, each discounted by (1 + y/2) for every half-year until it arrives, add up to that price. The price is our estimate from the Treasury's par curve, not a dealer quote, and for a TIPS the yield is a real yield, the rate above inflation.
Worked example
- UST 4.625% 2036-08-15, a Treasury paying 4.625% a year, matures on 15 Aug 2036. Its estimated full price on the Treasury curve of 2 Oct 2026 is 95.611 per 100, with 20 payments still to come.
- The yield to maturity is the single yearly rate, compounded twice a year, at which those 20 payments are worth exactly that price today: 5.28%.
- It is what the bond yields only if it is held to maturity, every payment arrives and every coupon is reinvested at that same rate: a way of stating today's estimated price, not a return anyone is owed.
Real Treasuries valued today on the Treasury's par curve: our estimates, not dealer quotes, and no yield here is a return anyone is owed. The demo holds none; signed in with a Treasury of your own, this is worked on yours.
Where it misleads
It is a way of stating today's price, not a return anyone is owed. It is what the bond would yield only if it is held to maturity, every payment arrives and every coupon is reinvested at that same rate; sell earlier, or reinvest at another rate, and the result differs. Two bonds with the same yield can also move very differently when rates change.
The formula
- P — the full price per 100 of face value (clean price plus accrued interest);
- CFj — the j-th payment per 100: the coupon, and 100 more with the last one;
- y — the yield to maturity, a yearly rate compounded twice a year;
- w — the part of the current coupon period still to run: days to the next coupon divided by days in the period;
- n — the number of payments left.
A worked example on a real Treasury
The Treasury note UST 4.625% 2036-08-15 (ISIN US91282CRF04) is a 10-year note issued on 17 August 2026. On the Treasury par curve of 1 October 2026 its estimated full price is 95.896 per 100 of face value and 20 payments remain: 2.3125 every six months, and 102.3125 on 15 August 2036 (the last coupon plus the principal). Discounted at y = 5.2394 %, the first coupon is worth 2.268 today and the last payment 61.402; the twenty present values add up to 95.896. So its yield to maturity is 5.24 %, above its 4.625 % coupon because its price is below 100. It would be what the bond yields only if it is held until 15 August 2036, every payment arrives and every coupon is reinvested at 5.24 %. Every figure is our estimate from the Treasury curve, not a dealer quote, read on 2 October 2026.
What this page does not do
It does not say what you will earn, and it does not forecast anything: it restates the estimated price of today as a rate. The price moves every day with the Treasury curve, and so does the yield.
Compared with
- Clean and full price — the price without and with the accrued interest, the one the yield is solved from
- Modified duration — how much that price moves for a one-point change in yield
- Accrued interest — the part of the next coupon already earned
Questions people ask
Is the yield to maturity what I will earn on this Treasury?
No. It is the rate that reproduces today's estimated price if the bond is held to maturity, every payment arrives and every coupon is reinvested at that same rate. Selling earlier at another price, or reinvesting at other rates, gives another result.
Why is the yield different from the coupon?
The coupon is a fixed amount of the face value; the yield also reflects the price. A bond priced below 100, like the one above, has a yield above its coupon, because the holder also collects the difference up to 100 at maturity.
Sources
Last reviewed 2026-10-02 by Sphinx Risk.