Bond Yield to Maturity Calculator
Yield to maturity (YTM) is the most widely used measure of a bond's return. It represents the annualized rate of return an investor earns if the bond is purchased today and held until it matures, assuming all coupon payments are reinvested at the same rate. YTM incorporates the coupon income, the return of principal at maturity, and any capital gain or loss from buying the bond above or below its face value. This calculator uses the standard approximation formula to solve for YTM. For high-precision work, a financial calculator iterates to find the exact YTM, but the approximation is accurate within a few basis points for typical bonds.
YTM approximation formula
YTM = (C + (F - P) / n) / ((F + P) / 2)
where C = annual coupon, F = face value, P = price, n = years to maturity
This is the standard textbook approximation for annual YTM. The numerator adds the coupon to the amortized discount (or subtracts the amortized premium). The denominator is the average of face value and price, representing the average investment. For exact YTM, solve numerically for the rate r where P equals the present value of all future cash flows.
How to interpret YTM
- YTM above the coupon rate means the bond trades at a discount (below face value).
- YTM equal to the coupon rate means the bond trades at par (face value).
- YTM below the coupon rate means the bond trades at a premium (above face value).
- Comparing YTM across bonds with similar maturities and credit quality allows apples-to-apples return comparisons.
- The yield spread over US Treasury bonds of the same maturity reflects credit risk of the issuer.
Frequently asked questions
What is yield to maturity?
Yield to maturity (YTM) is the total return anticipated on a bond if it is held until it matures. YTM is expressed as an annual rate and accounts for coupon payments, the difference between purchase price and face value, and the time remaining to maturity.
How is YTM different from current yield?
Current yield is simply the annual coupon divided by the current price. YTM goes further by also accounting for any capital gain or loss you will experience when the bond matures at face value. YTM is a more complete measure of return.
What approximation formula is used here?
This calculator uses the standard approximation: YTM = (C + (F - P) / n) / ((F + P) / 2), where C is annual coupon, F is face value, P is price, and n is years to maturity. For exact YTM, iterative methods or financial calculators are used, but this approximation is accurate to within a few basis points for most bonds.
If a bond trades at a premium, is YTM above or below the coupon rate?
If a bond trades above face value (at a premium), the YTM is below the coupon rate because you will receive less than you paid when the bond matures. If it trades at a discount, YTM exceeds the coupon rate.
Where can I find bond prices and face values?
US Treasury bond prices are published by the U.S. Treasury at TreasuryDirect.gov. Corporate and municipal bond prices are available through FINRA's TRACE system and broker platforms. The SEC's EDGAR database provides bond prospectuses.
Official sources
- U.S. Treasury: TreasuryDirect - Bond Prices and Yields.
- SEC EDGAR: Bond Prospectuses (EDGAR).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.