Audited —·Last updated 27 Jul 2026·6 citations·Tier 1·0 uses

Bond Yield to Maturity Calculator

Solve bond yield to maturity from price, coupon, face value, compounding frequency, and years to maturity.

Bond Yield to Maturity Calculator

Coupon Payments per Year
Nominal Annual Yield to Maturity
6.18
Coupon Payment per Period
25.00
Number of Coupon Periods Remaining
10
Current Yield
5.26
Periodic Yield per Coupon Period
3.09
Effective Annual Yield
6.27
Present-Value Price Check
950.00
Premium or Discount to Face Value
50.00

Background.

A bond yield to maturity calculator solves the annualized discount rate that makes a bond's promised future cash flows equal to its current price. The canonical use case is an investor comparing a coupon bond selling below par with its stated coupon rate. A five-year bond with 5 percent annual coupon, paid semiannually, face value 1,000, and price 950 does not have a 5 percent yield to maturity. Because the investor pays less than face value and receives coupons plus 1,000 at maturity, the yield is higher than the coupon rate. Solving the cash-flow equation gives a nominal semiannual-compounded YTM of 6.177624640903 percent.

People search for this calculator because bond vocabulary is compact but non-intuitive. Coupon rate is the cash interest rate based on face value. Current yield is annual coupon divided by current price. Yield to maturity is the internal rate of return implied by price, coupons, redemption value, and time to maturity, assuming payments are made as scheduled and the bond is held to maturity. Those are different concepts. A bond can have a 5 percent coupon, a 5.263158 percent current yield, and a 6.177625 percent nominal YTM at the same time.

Regulators and market infrastructure bodies emphasize these distinctions. SEC Investor.gov explains bond basics and how prices and interest rates move. FINRA explains how bond prices, rates, and yields relate and discusses yield to maturity as a common bond yield measure. The MSRB's municipal-bond education material describes yield to maturity and other yield concepts for investors. TreasuryDirect explains marketable Treasury securities, prices, interest, and yields. These sources do not make yield arithmetic optional; they show why a transparent solver matters for investor understanding.

The calculation is a present-value equation. Each future coupon is discounted back at the periodic yield. The redemption payment is also discounted. The periodic yield is the unknown. Because it appears in powers from one period through the final period, the equation usually cannot be solved by simple algebra for ordinary coupon bonds. A calculator should use a numerical method such as bisection or Newton-Raphson and then verify the result by repricing the bond. In the worked example, the coupon present value is 212.291753515198 and the redemption present value is 737.708246484802. Their sum is exactly 950 at the displayed periodic yield.

For Quanta, the most important implementation details are clarity and numerical stability. Inputs should include price, face value, coupon rate, years to maturity, coupon frequency, and optional redemption value. Outputs should distinguish current yield, periodic yield, nominal annual YTM, and effective annual yield. The solver should handle premium bonds, discount bonds, zero-coupon bonds, and short maturities. It should warn that realized return can differ from YTM if the bond is sold before maturity, the issuer defaults, the bond is called, or coupon reinvestment differs from the assumed yield.

The worked example deliberately uses semiannual coupons because many bonds pay twice per year. The periodic yield is 3.0888123204515 percent. Multiplying by two gives nominal annual YTM of 6.177624640903 percent. Compounding the two periods gives an effective annual yield of 6.273032256413 percent. Investors should know which convention a quote uses before comparing bonds.

What is bond yield to maturity calculator?

Yield to maturity is the discount rate that equates a bond's current price with the present value of all promised future coupon and principal payments, assuming the bond is held to maturity and payments are made as scheduled. It is often quoted as an annual percentage, with a convention tied to coupon frequency. For a semiannual bond, the solved six-month yield is commonly doubled to report nominal annual YTM, while effective annual yield compounds it.

The key terms are price, par value, face value, coupon rate, coupon payment, maturity, redemption value, current yield, periodic yield, nominal YTM, effective annual yield, premium, and discount. Price is what the investor pays. Face value is the amount used to calculate coupons and often repaid at maturity. Coupon rate is the annual rate on face value. Current yield is coupon income divided by price. YTM includes coupon income and the gain or loss from price moving to redemption value.

The calculator is valid for fixed-rate bonds with known coupon frequency and redemption value. It does not model default probability, taxes, accrued interest, call options, sinking funds, floating rates, inflation-indexing, amortizing principal, callable municipal-bond yield-to-worst, or reinvestment outcomes unless those modes are added separately.

How to use this calculator.

  1. Enter the bond price per face value.
  2. Enter face value or par value.
  3. Enter the annual coupon rate.
  4. Enter years to maturity.
  5. Enter coupon payments per year.
  6. Enter redemption value if it differs from face value.
  7. Review current yield, periodic yield, nominal YTM, effective annual yield, and price check.

The formula.

P = C × [ 1 − (1+r)⁻ⁿ ] ⁄ r + R ⁄ (1+r)ⁿ
P · bond priceC · coupon per periodr · periodic yield (solved)n · # of periodsR · redemption value

The price of a fixed coupon bond is the present value of its coupon payments plus the present value of its redemption payment. If the annual coupon rate is 5 percent on a 1,000 face value bond paid twice per year, the annual coupon is 50 and each semiannual coupon is 25. Five years to maturity with two payments per year gives 10 periods. The cash flows are nine payments of 25 and a final payment of 1,025, which includes the last coupon plus redemption value.

Yield to maturity is found by choosing the periodic discount rate that makes those cash flows worth today's price. If r is the six-month rate, price equals 25 divided by 1 + r for the first coupon, plus 25 divided by (1 + r)^2 for the second coupon, continuing through period 10, plus 1,000 divided by (1 + r)^10. The annuity formula compresses the coupon stream into couponPayment times (1 - (1 + r)^-periods) divided by r. The redemption value remains a separate discounted lump sum.

The unknown r is inside exponents and denominators, so the calculator should solve numerically. Bisection is slow but robust: choose a low and high yield, compute present value at the midpoint, and narrow the interval until the price error is tiny. Newton-Raphson is faster but can fail with poor starting points or unusual cash flows. Engineering can use either method if it returns a price check near the input price.

After solving r, conventions matter. Nominal YTM for a semiannual bond is r times 2. Effective annual yield is (1 + r)^2 minus 1. In the example, r is 0.030888123204515. Nominal YTM is 6.177624640903 percent, while effective annual yield is 6.273032256413 percent. Current yield is simpler: annual coupon divided by price, or 50 divided by 950, which is 5.263158 percent. Current yield ignores the 50-point discount accretion to maturity, so it is lower than YTM.

The calculator should preserve full precision internally and round display values only at the UI layer. Small rounding differences in periodic yield can move the price check by cents or more.

A worked example.

Example

The example bond has a 1,000 face value, a 5 percent annual coupon, semiannual payments, five years to maturity, and a price of 950. The annual coupon is 50, so each semiannual coupon is 25. Five years times two payments per year gives 10 periods. Current yield is annual coupon divided by price: 50 divided by 950 equals 5.26315789473684 percent. Yield to maturity requires solving the present-value equation. At the periodic yield 0.030888123204515, the coupon annuity factor is 8.4916701406079. Multiplying by the 25 coupon gives coupon present value of 212.291753515198. The 1,000 redemption payment discounted for 10 periods is 737.708246484802. Adding those values gives 950, matching the input price. The periodic yield is 3.0888123204515 percent. Doubling it for a semiannual nominal quote gives 6.177624640903 percent. Compounding the two periods gives an effective annual yield of 6.27303225641274 percent.

annual Coupon Rate Percent5
payments Per Year2
years To Maturity5
face Value1,000
price950
redemption Value1,000

Frequently asked questions.

Why is yield to maturity different from coupon rate?
Coupon rate is fixed as a percent of face value. Yield to maturity depends on the price paid, coupon payments, time to maturity, and redemption value. If a bond sells below face value, the investor earns coupons plus a gain as the bond moves toward redemption, so YTM can exceed the coupon rate. If a bond sells above face value, YTM can be below the coupon rate. The calculator solves the full cash-flow equation rather than assuming coupon rate equals return.
Why is current yield not enough?
Current yield divides annual coupon income by price, but it ignores the gain or loss from the bond's price moving toward redemption value. In the example, current yield is 5.263158 percent, while nominal YTM is 6.177625 percent because the investor also receives 1,000 at maturity after paying 950. Current yield is useful for income comparison, but it is not a complete held-to-maturity return measure.
What does semiannual compounding mean?
Semiannual compounding means coupons are paid twice per year and the solved periodic yield is a six-month rate. Market convention often reports nominal annual YTM as two times the six-month rate. Effective annual yield compounds the two six-month periods. In the example, the six-month rate is 3.088812 percent, nominal YTM is 6.177625 percent, and effective annual yield is 6.273032 percent. The calculator should show both conventions to avoid confusion.
Does YTM assume coupons are reinvested?
YTM is the internal rate implied by scheduled cash flows and price. A common interpretation assumes coupons can be reinvested at the YTM rate to realize that compound return. If actual reinvestment rates are lower or higher, realized return can differ. If the bond is sold before maturity, market price changes can also change realized return. The calculator should label YTM as an implied yield, not a guaranteed future return.
Can this calculator handle zero-coupon bonds?
Yes if coupon rate is zero and the solver handles a zero coupon stream. The price equation becomes redemption value divided by (1 + periodicYield)^periods. A direct formula is also possible for zero-coupon bonds: periodicYield equals (redemptionValue / price)^(1 / periods) minus one. Engineering can route zero coupons through the general solver or use the closed form as a stable special case.
What about callable bonds?
Callable bonds need yield-to-call and yield-to-worst analysis because the issuer may redeem the bond before maturity. Yield to maturity can overstate the investor's likely return when a premium bond is likely to be called. FINRA and MSRB investor education materials emphasize understanding call features and yield measures. This calculator is for yield to stated maturity. A callable-bond module should add call dates, call prices, and worst-yield comparisons.
Should I use clean price or dirty price?
The present-value equation prices future cash flows from the settlement date. Market quotes often use clean price, which excludes accrued interest, while the actual invoice amount includes accrued interest. A simple YTM calculator that ignores accrued interest should state whether the entered price is clean or dirty and how settlement is treated. For precise bond math, engineering would need settlement date, coupon dates, day-count convention, accrued interest, and market convention.
When should I not use this calculator?
Do not use it as the sole analysis for callable bonds, floating-rate notes, inflation-indexed bonds, amortizing bonds, distressed debt, tax-exempt after-tax comparisons, or bonds with irregular first or last coupon periods. It also does not model credit risk, liquidity, taxes, or reinvestment. Use it for fixed-rate bonds with known price, coupon, maturity, frequency, and redemption value, then apply security-specific risk analysis separately.

References& sources.

  1. [1]U.S. Securities and Exchange Commission (n.d.). Bonds. Investor.gov.
  2. [2]Financial Industry Regulatory Authority (n.d.). Bond Yield and Return. FINRA.
  3. [3]Financial Industry Regulatory Authority (n.d.). Understanding Bond Prices, Rates and Yields. FINRA.
  4. [4]Municipal Securities Rulemaking Board (n.d.). Bond Basics. MSRB Education Center.
  5. [5]Municipal Securities Rulemaking Board (n.d.). Yield. MSRB Education Center.
  6. [6]U.S. Department of the Treasury (n.d.). Treasury Bonds. TreasuryDirect.
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