Yield to Maturity Calculator

What yield to maturity measures

Yield to maturity is the single interest rate that makes the present value of every payment a bond will make land exactly on the price you pay for it. Discount each coupon and the face value back to today, add the pieces, and the rate that makes the total equal your purchase price is the yield to maturity, or YTM.

The SEC's investor education office describes it as the annual return on a bond if it is held to maturity, taking into account when you bought it and what you paid (SEC Investor Bulletin: What Are Corporate Bonds?, 2026). Three parts of that sentence carry weight. You hold the bond to the end. The issuer pays every coupon on schedule. And each coupon gets reinvested at the same yield, which is the part most readers skip.

The coupon rate never moves. A 5% bond pays $50 a year on a $1,000 face value no matter what the market does. YTM moves with the price instead, and the price changes every trading day. That is why the same bond can carry a 5% coupon and a 5.66% yield once you buy it at $950 instead of $1,000.

The price formula, term by term

Every bond price starts from one line of arithmetic:

Price = C/(1+r) + C/(1+r)^2 + ... + C/(1+r)^n + F/(1+r)^n

C is the coupon paid each period, F is the face value, n is the number of coupon periods left, and r is the yield per period. A $1,000 face value with a 5% annual coupon paid twice a year gives C = $25, and 10 years to maturity gives n = 20 periods.

Set the price to $950 and the line turns into a puzzle. The rate r appears in all 20 denominators, and no rearrangement isolates it. Clear the fractions and you get a degree 20 polynomial in (1+r), and those have no closed form solution. Every serious YTM figure, from a spreadsheet's RATE function to a trading terminal, comes from a numeric solver of one kind or another.

The 20 coupons contribute $377.82 of the $950 price and the face value contributes the other $572.18. Same total, two pieces, and the split between them moves whenever the yield does.

Why this calculator solves by bisection instead of a shortcut

Textbooks offer a shortcut: YTM is roughly (C + (F - P)/n) / ((F + P)/2), where C is the annual coupon, F is the face value, P is the price and n is the years left. It needs four numbers, it runs in one line, and it lands close on a bond trading near face value.

Close is not exact, and the gap widens as the price moves away from face:

Bisection works the way a person would. Pick a rate that is too low and one that is too high, test the midpoint, and see whether the resulting price is above or below what you paid. Bond price falls as the rate rises, so each midpoint test says which half of the bracket to keep. Two hundred rounds shrink the bracket to a width of about 10^-58, far past any decimal a bond quote carries, and the result reproduces the RATE function in a spreadsheet.

Worked example: a 5% bond bought at $950

Take the default case in the calculator: a $1,000 face value, a 5% annual coupon paid twice a year, 10 years to maturity, and a purchase price of $950.

Solved by bisection on the price formula, the semiannual rate is 2.8308%, so the annual yield is 5.66% on the bond quoting convention, or 5.74% if you compound the two halves instead of adding them. Everything else on the results panel follows:

In dollars the whole schedule reads 20 x 25 = 500 of coupons, plus 1,000 - 950 = 50 of gain at maturity, for $550 back on a $950 outlay.

Two lines in that table deserve a second look. Current yield is 50 / 950 = 5.26%, which counts the coupon against the price and stops there. Total return is (500 + 50) / 950 = 57.89% over the whole holding period, which counts every dollar received against every dollar paid. Spread across 10 years that compounds to 4.67% a year. The gap to 5.66% is the reinvestment assumption at work: YTM sends each $25 coupon back in at 5.66%, while the simple total return lets coupons sit idle.

Premium, par and discount: three prices, one bond

The same coupons and the same maturity can produce three different yields. Price is the only thing that changes.

The pattern is fixed. Buy below face and the yield to maturity runs above the coupon rate, because you pocket the gap at maturity on top of the coupons. Buy at face and the two rates match. Buy above face and the yield runs below the coupon rate, because the $50 you give back at maturity works against the $500 you collect along the way. The premium bond still earns 42.86% over the decade, just less than the 50% the coupons alone would suggest.

That pull toward face value is what draws the curve in the figure above: in the middle of the range, a 1% move in yield moves the price by about $80, and the curve keeps sliding toward the face value line as yields climb.

Current yield, coupon rate and YTM compared

Each number answers a different question. The coupon rate is what the bond was built to pay. Current yield counts the coupon against today's price and stops there. Yield to maturity adds the gain or loss at maturity and the time value of every payment.

Current yield has a known blind spot: it ignores the $50 gain entirely. On a deep discount bond that blind spot gets expensive. A 2% coupon bond bought at $700 shows a 2.86% current yield but a 3.65% yield to maturity, and the difference is the $300 of gain the current yield never sees.

What YTM assumes, and where it stops being true

The number carries four assumptions, and each one can break.

• Reinvestment. Every coupon is assumed to go back to work at the same YTM. In 2026, with money market accounts and short Treasury bills paying their own rates, the coupon rarely lands at exactly the yield on the bond it came from. If reinvestment happens at a lower rate, the realized return lands below the printed YTM.
• Hold to maturity. Sell early and the yield becomes a realized yield that depends on the selling price. A bond bought at $950 and sold at $980 after a year locks in most of its capital gain in 12 months and gives up the rest of the schedule.
• The issuer pays. YTM treats every coupon as certain. Corporate bonds carry default risk, so the promised yield and the expected yield are not the same number. SEC Investor Bulletin: Interest Rate Risk walks through how prices and yields move together when rates change.
• Fixed coupons. A callable bond lets the issuer retire it early, usually when rates have fallen. Then the bond disappears years ahead of schedule, and the honest return is the yield to call, or the yield to worst across every call date. Premium bonds carry the most call risk, which is one reason the market demands extra yield from them.

Zero coupon bonds sidestep the reinvestment assumption entirely: nothing to reinvest, and the whole return is the gap between purchase price and face value.

Where to check Treasury yields in 2026, and the tax angle

The Treasury publishes its Daily Treasury Par Yield Curve Rates every business day (U.S. Department of the Treasury, 2026). The curve covers constant maturity points at 1, 1.5, 2, 3, 4 and 6 months and 1, 2, 3, 5, 7, 10, 20 and 30 years, built from bid side quotes on recently auctioned securities. Those par yields are the public benchmark for what a 10 year bond should yield on a given morning.

Savings bonds are quoted differently, and TreasuryDirect's rates page lists them directly. For bonds issued May 1 through October 31, 2026, Series EE bonds pay a fixed 2.40% and Series I bonds pay a composite 4.26%. Neither is a market yield; both are set by rule twice a year.

The tax side lives in IRS Publication 550 (2025), which covers interest income and how the discount on a bond bought below face gets reported. The short version: coupons are taxed as ordinary interest, while the discount on a bond bought below face follows market discount or capital gain rules depending on the bond and the holding period. This page is a calculator, not tax advice, so confirm the figures that matter with the publication itself.