Bond Parameters

$
Par value paid at maturity
%
Enter as percentage (e.g., 5 for 5%)
$
Clean price (excludes accrued interest)
years
Time remaining until bond matures
Most U.S. bonds pay semi-annually

Bond Pricing Formula

P = Σ [C/m ÷ (1 + y/m)t] + F ÷ (1 + y/m)mn
P = Price | C = Annual coupon | F = Face value | y = YTM | m = Frequency | n = Years
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Bond Yield Results

Yield to Maturity (Bond-Equivalent Yield) --
Current Yield --
Coupon Payment --
Total Coupon Income --
Price vs. Par --

Formula Breakdown

P = Σ [C/m ÷ (1 + y/m)t] + F ÷ (1 + y/m)mn
Solve for y (YTM) given the bond's market price

Model Assumptions

  • Fixed-rate coupon bond (not floating or inflation-linked)
  • Reinvestment of coupons at the YTM rate (standard BKM assumption)
  • No embedded options affect pricing (unless callable toggle is on)
  • Clean price input (excludes accrued interest)
  • Flat yield curve (single discount rate for all cash flows)
  • For educational purposes. Not financial advice. Market conventions simplified.

Understanding Yield to Maturity

Video Explanation

Video: Yield to Maturity Explained

What is Yield to Maturity?

Yield to maturity (YTM) is the total return anticipated on a bond if held until it matures. It is the internal rate of return (IRR) of the bond's cash flows, assuming all coupon payments are reinvested at the same rate. YTM accounts for the bond's current market price, face value, coupon rate, and time to maturity.

Bond Pricing Equation (Solved for YTM)
P = Σ [C/m ÷ (1 + y/m)t] + F ÷ (1 + y/m)mn
Solve for y such that the present value of all cash flows equals the market price P

Key Concepts

Price-Yield Relationship

Bond prices and yields move inversely. When rates rise, prices fall (and vice versa). This relationship is convex, meaning price increases from rate drops exceed price decreases from equal rate increases.

Current Yield vs. YTM

Current yield (Coupon/Price) only measures income return. YTM captures income, capital gain/loss, and reinvestment, making it a more complete measure of expected return.

Yield to Call

For callable bonds, the issuer can redeem the bond before maturity at a specified call price. Yield to call (YTC) calculates the return assuming the bond is called at the earliest call date. Investors use the lower of YTM and YTC, known as yield to worst (YTW), for conservative analysis.

Important: YTM assumes reinvestment of all coupons at the YTM rate. Actual realized returns will differ if reinvestment rates change over the bond's life. This reinvestment risk is a key limitation of YTM as a return measure.

Related Reading

Frequently Asked Questions

Yield to maturity (YTM) is the total return anticipated on a bond if held until it matures. It is the internal rate of return (IRR) that equates the present value of all future coupon payments and the face value repayment to the bond's current market price. YTM assumes all coupons are reinvested at the same rate and the bond is held to maturity with no default.

Current yield only considers the annual coupon payment relative to the bond's current price (Annual Coupon / Price). It ignores the time value of money, capital gains or losses from buying at a discount or premium, and reinvestment income. YTM captures all three components, making it a more comprehensive measure of a bond's expected return.

Bond prices and yields move inversely. When market interest rates rise, existing bond prices fall (and YTM rises). When rates fall, bond prices rise (and YTM falls). This inverse relationship is convex, meaning price increases from rate decreases are larger than price decreases from equal rate increases. Longer-maturity bonds are more sensitive to yield changes.

Yield to call (YTC) is the yield assuming the bond issuer calls (redeems) the bond at the first call date rather than letting it mature. YTC matters for callable bonds trading at a premium, where the issuer has an incentive to refinance at lower rates. Investors should compare YTM and YTC and use the lower value (yield to worst) for conservative analysis.

For coupon-paying bonds, YTM requires solving a polynomial equation where the yield appears in multiple terms raised to different powers. There is no closed-form algebraic solution for this type of equation when there are more than a few cash flows. Instead, numerical methods like bisection or Newton-Raphson iteration are used to find the yield that makes the present value of cash flows equal to the market price.

Yes, YTM implicitly assumes that all coupon payments are reinvested at the YTM rate for the remaining life of the bond. This is a key limitation because actual reinvestment rates will vary over time. If rates fall, reinvestment income will be lower than YTM implies. This reinvestment risk is why realized returns often differ from the YTM calculated at purchase.
Disclaimer

This calculator is for educational purposes only and assumes a fixed-rate coupon bond with clean price input. Actual bond yields depend on accrued interest, day-count conventions, and settlement dates. Results use the bond-equivalent yield (BEY) convention. This tool should not be used for trading decisions.

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Master fixed income investing from fundamentals to advanced strategies. Covers bond pricing, duration, convexity, yield curves, and interest rate risk management.

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