Yield to Maturity Calculator
A $950 bond with a $1,000 face value, a 5% coupon, 10 years left, and semiannual coupons has a yield to maturity of about 5.66%. This yield to maturity calculator estimates the annualized return on a plain fixed-coupon bond when you buy at today's price and hold it to maturity. Enter the bond price, face value, coupon rate, years to maturity, and payment frequency to see the bond's nominal YTM, periodic yield, and current yield.
Quick answer
Yield to maturity is the discount rate that makes the bond's coupon payments and maturity value add up to the current price.
What this tells you
- •Yield to maturity is the discount rate that makes the bond's coupon payments and maturity value add up to the current price.
- •If the bond price is below face value, YTM is usually above the coupon rate. If the price is above face value, YTM is usually below the coupon rate.
- •This calculator reports YTM as a nominal annual rate compounded at the coupon payment frequency.
- •It solves the full present-value equation by bisection rather than using the common shortcut approximation.
- •YTM is conditional on all promised payments and holding to maturity, not a guaranteed realized return.
How to Use
- 1Enter the current bond price in dollars for one bond, not as a percent-of-par quote.
- 2Enter the face value, which is often $1,000 for many US bonds.
- 3Enter the annual coupon rate as a percent, such as 5 for a 5% coupon.
- 4Enter the years left to maturity and choose how many coupon payments the bond makes each year.
- 5Calculate to see the estimated yield to maturity, periodic yield, current yield, and coupon cash flow details.
How It Works
Formula
Price = Σ [Coupon payment ÷ (1 + r)^t] + [Face value ÷ (1 + r)^n]
Coupon payment = Face value × coupon rate ÷ payments per year
Nominal YTM = periodic rate r × payments per yearThe bond price equals the present value of every fixed coupon payment plus the present value of the face value paid at maturity. Because the periodic yield sits inside each discount factor, the calculator solves for that rate with a deterministic bisection search. The model assumes equal coupon periods and settlement on a coupon date.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Discount bond with a higher YTM than the coupon rate
The bond pays $25 every six months and returns $1,000 at maturity. Because you buy it below face value, the yield to maturity ends up above the 5% coupon rate.
Premium bond with a lower YTM than the coupon rate
This bond pays only $30 a year in coupons but costs $100 above face value today. That premium drags the yield to maturity below the 3% coupon rate.
10-Year 5% Coupon Bond at Different Prices
These examples use a $1,000 face value bond with semiannual coupon payments so you can see how price changes YTM.
| Bond price | Current yield | Estimated YTM |
|---|---|---|
| $900 | 5.56% | 6.37% |
| $950 | 5.26% | 5.66% |
| $1,000 | 5.00% | 5.00% |
| $1,050 | 4.76% | 4.38% |
| $1,100 | 4.55% | 3.79% |
These figures assume fixed coupons, no accrued interest, and maturity exactly on the final coupon date. Real bond quotes can use clean prices and settlement conventions that shift the result.
How the solver and yield outputs work
The coupon payment equals face value times annual coupon rate divided by payments per year. A $1,000 face bond with a 5% coupon and two payments pays $25 each period. The number of periods must equal years to maturity times frequency as a whole number. A term that lands between coupon periods is rejected because the model has no accrued-interest or stub-period calculation.
The solver searches for the periodic discount rate that makes the modeled cash flows equal the entered price. It starts just above a negative 100% periodic rate and expands the positive upper bound when needed. It then performs 200 bisection iterations. This is the full fixed-cash-flow equation, not the shortcut approximation based on average price and annual gain or loss.
Bisection is deterministic for the ordinary cash-flow pattern modeled here, but a numerical method still has a domain. The implementation can return no result for invalid inputs, misaligned periods, nonfinite arithmetic, or a price that cannot be bracketed within its search bound. A successful convergence only means the programmed equation has been solved, not that the cash flows are certain.
Periodic yield is the rate for one coupon interval. Nominal YTM multiplies that periodic rate by payments per year. Effective annual yield compounds the periodic rate across the year. Two bonds can show the same nominal rate yet have a different effective rate when their frequencies differ. Compare yields on the same convention.
Current yield is annual coupon dollars divided by price. It ignores the gain or loss between purchase price and face value, plus the time remaining until maturity. YTM includes those modeled cash flows. Neither measure deducts taxes, transaction fees, bid-ask spread, custody costs, or accrued interest.
The input price must be in the same dollar scale as face value. A quote of 95 often represents 95% of par, which becomes $950 for $1,000 face value. Market quotes may be clean prices that omit accrued interest. This model assumes the entered price is the cash price at a coupon date, so an actual settlement may require dirty price, day-count, and calendar adjustments.
YTM assumes coupons can be reinvested at the calculated yield for the relevant realized-return interpretation. Future reinvestment rates can differ. Selling before maturity introduces market-price risk, while default or restructuring can change coupons and principal. Callable, putable, convertible, inflation-linked, floating-rate, amortizing, and sinking-fund securities need cash-flow models suited to their terms.
Negative YTM is mathematically possible when price is high relative to remaining cash flows. The solver permits a periodic rate above negative 100%. A negative modeled yield is not a statement about tax treatment, market liquidity, or whether the bond is appropriate. Verify unusual results against current security data and a professional source.
Common mistakes
- Entering a quote like 95 instead of the dollar price, which would be $950 on a $1,000 face bond
- Assuming yield to maturity must match the coupon rate even when the bond trades above or below face value
- Using this simple fixed-coupon model for callable, putable, or off-cycle settlement bonds
- Entering a clean quoted price without adding accrued interest when the intended equation needs the dirty settlement price
- Comparing nominal YTM with an effective annual yield as though the compounding conventions were identical
- Treating YTM as a promised return despite default, call, sale-price, and reinvestment risk
Limitations
This calculator models a plain fixed-coupon bond with equal periods, fixed coupons, one face-value payment at maturity, and settlement on a coupon date. Years times payment frequency must be a whole number. The entered price is used directly and is assumed to share the face-value currency scale. It does not handle clean-versus-dirty pricing, accrued interest, settlement dates, day-count conventions, holidays, odd coupons, amortization, floating rates, inflation linkage, calls, puts, conversions, sinking funds, defaults, recovery, taxes, fees, bid-ask spreads, liquidity, currency risk, or reinvestment rates. Numerical convergence solves only the stated cash flows and does not guarantee realized return.
Embed this calculator on your site
Drop this single line where you want the calculator to appear. It is responsive, mobile-friendly, resizes automatically, and is free to use with attribution.
<script src="https://calctide.com/embed.js" data-tool="yield-to-maturity-calculator" async></script>Preview the embed at /embed/yield-to-maturity-calculator/.