Why is a discount bond's YTM higher than its coupon rate?

A discount bond trades below face value, meaning you pay less than $1,000 for a $1,000 bond. At maturity, you receive the full face value -- producing a capital gain. That gain, spread over the remaining years, adds to the effective annual return above the coupon rate. Conversely, a premium bond's YTM is below its coupon rate because the capital loss at maturity (paying above $1,000 to receive $1,000) partially offsets the coupon income.

What is the difference between YTM and YTC?

YTM (yield to maturity) assumes the bond is held until its stated maturity date. YTC (yield to call) assumes the bond is called by the issuer at the earliest call date and call price. For bonds trading above par, YTC is typically lower than YTM because the investor receives the call price (often par) sooner than maturity. Callable bond investors should consider the lower of YTM and YTC as the most conservative return estimate.

What is the tax-equivalent yield for a municipal bond?

Tax-equivalent yield = Municipal bond YTM / (1 - your marginal federal tax rate). A 3.8% municipal bond for a taxpayer in the 37% bracket has a tax-equivalent yield of 3.8% / (1 - 0.37) = 6.03%. This means a taxable bond would need to yield 6.03% to deliver the same after-tax return as the 3.8% municipal bond.

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Bond Yield to Maturity Calculator

Calculate bond YTM from face value, coupon rate, current market price, and years to maturity with current yield and total return projections.

Face (Par) Value ($)

Current Market Price ($)

Annual Coupon Rate (%)

Years to Maturity

Coupon Payments Per Year

Most U.S. corporate and Treasury bonds pay semi-annually. Municipal bonds also typically pay semi-annually.

Bond Yield Analysis

Enter bond details and click calculate.

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Introduction

A bond's coupon rate and its actual return are not the same number. A bond with a 5% coupon rate purchased at $920 (below its $1,000 face value) delivers a yield to maturity of approximately 6% -- because the buyer also collects the $80 discount as a capital gain at maturity. Conversely, a bond bought at $1,080 (a premium) delivers a YTM below its 5% coupon because the investor loses $80 at maturity. Current yield, the simpler metric, misses this entirely. According to FINRA BondFacts, YTM is the most comprehensive measure of bond return because it accounts for coupon income, time value of money, and the capital gain or loss from buying at a discount or premium. In 2026, with 10-year Treasuries yielding approximately 4.2% to 4.5% and investment-grade corporates at 5.0% to 5.5%, understanding YTM is essential for comparing bonds and evaluating whether the promised return compensates for the credit and duration risk.

What This Calculator Does

This bond yield to maturity calculator determines the total annualized return (YTM) you will earn if you purchase a bond today and hold it until maturity, given the face value, coupon rate, current market price, years to maturity, and coupon payment frequency. It also calculates current yield (annual coupon / current price), total coupon income over the holding period, capital gain or loss at maturity, and total dollar return. Both semi-annual and annual coupon structures are supported.

The Formula

YTM is the rate (r) solving: Price = Sum of [Coupon / (1+r)^t for t=1 to n] + Face Value / (1+r)^n | Current Yield = Annual Coupon / Current Price

YTM is mathematically equivalent to the Internal Rate of Return (IRR) of the bond's cash flows. It is the single discount rate that makes the present value of all future coupon payments plus the face value repayment exactly equal to the current market price. No closed-form algebraic solution exists, so the calculation uses numerical iteration (bisection method or Newton-Raphson) to converge on the rate. Semi-annual coupon bonds divide the annual coupon by 2 and use semi-annual periods; YTM is then annualized by multiplying the semi-annual rate by 2 (or compounding it for the effective annual rate).

Step-by-Step Example

Enter bond characteristics

Face value: $1,000. Coupon rate: 5% annual ($50/year). Frequency: semi-annual ($25 per payment). Years to maturity: 8 years (16 semi-annual periods). Current market price: $940 (discount bond -- below face value).

Calculate current yield

Current yield: $50 annual coupon / $940 price = 5.32%. This is simpler but incomplete -- it ignores the $60 capital gain at maturity.

Iteratively solve for YTM

The YTM is found by solving: $940 = Sum of [$25 / (1+r/2)^t] for t=1 to 16, plus $1,000 / (1+r/2)^16. The iterative solution converges to r/2 = 2.92%, so semi-annual YTM = 2.92%, annualized YTM = 5.84%.

Interpret the result

YTM: 5.84%. Current yield: 5.32%. The 0.52% difference is the contribution of the $60 discount (capital gain) spread over 8 years. Total coupon income: $50 x 8 = $400. Capital gain at maturity: $60. Total return: $460 over 8 years.

Real-World Use Cases

Comparing Two Bonds for Portfolio Inclusion

Bond A: 6% coupon, $1,050 price, 10 years to maturity. Bond B: 4% coupon, $870 price, 10 years to maturity. Current yields: 5.71% (A) and 4.60% (B). YTMs: approximately 5.48% (A) and 5.54% (B). Despite Bond A's higher current yield, Bond B offers a slightly higher YTM because the deeper discount produces a larger capital gain at maturity. YTM is the correct comparison metric.

Treasury Bond Ladder Construction

A fixed-income investor builds a 5-year ladder with Treasury bonds maturing in 1, 2, 3, 4, and 5 years. Computing the YTM for each rung ensures they know the guaranteed return for each maturity, allowing them to optimize the ladder for current yields and plan reinvestment timing.

Callable Bond Yield Comparison

A corporate bond offers 7% coupon at $1,020 with 12 years to maturity but a call date in 3 years at par ($1,000). YTM to maturity: 6.85%. Yield to call (YTC): 6.51%. If the company is likely to call the bond when rates fall, the effective return is closer to YTC -- the lower figure -- not the headline YTM. This calculator computes YTM; YTC requires entering the call date and call price as your maturity parameters.

Comparison

Bond Type	2026 Typical YTM	Credit Risk	Liquidity	Notes
US Treasury 2-Year	~4.0% to 4.2%	None (sovereign)	Highest	Benchmark short-term risk-free rate
US Treasury 10-Year	~4.2% to 4.5%	None (sovereign)	Highest	Benchmark intermediate rate; 10Y/2Y spread signal
AAA Corporate (10Y)	~4.8% to 5.0%	Minimal	High	Small spread over Treasuries for highest-rated issuers
A-rated Corporate (10Y)	~5.0% to 5.5%	Low to moderate	Good	Typical investment-grade corporate bond
BBB Corporate (10Y)	~5.5% to 6.0%	Moderate	Good	Lowest investment-grade tier; 'crossover' risk
High-yield / Junk (BB/B)	~7.0% to 8.5%	High	Moderate	Significant default risk; spreads widen in recessions
Municipal Bond (A-rated)	~3.5% to 4.5%	Low to moderate	Moderate	Tax-exempt; compare tax-equivalent yield to Treasuries

Common Mistakes to Avoid

Comparing current yield instead of YTM across bonds. Current yield ignores whether a bond was purchased at a discount or premium. Two bonds with the same current yield can have very different YTMs depending on their time to maturity and purchase price.
Ignoring call risk on callable bonds. Many corporate and municipal bonds are callable, meaning the issuer can redeem them at a set price before maturity. If interest rates fall and the bond is called, you will not receive the YTM you calculated assuming full maturity -- you will receive the (typically lower) yield to call.
Not accounting for taxes on coupon income. Bond interest is generally taxed as ordinary income. A 6% corporate bond in the 32% tax bracket delivers only 4.08% after federal tax. Municipal bond interest is typically federal tax-exempt; the tax-equivalent yield makes the comparison fair: TEY = Municipal YTM / (1 - Tax Rate).
Assuming all YTM is reinvestable at the same rate. YTM mathematically assumes all coupon payments are reinvested at the YTM rate. If rates fall, reinvestment of coupons at lower rates reduces actual compound return below the quoted YTM.

Frequently Asked Questions

Accuracy and Disclaimer

YTM calculations assume the bond is held to maturity with no default, all coupon payments are received as scheduled, and coupons are reinvested at the YTM rate. Actual returns may differ due to interest rate changes, credit events, early call, and reinvestment rate variation. Bond prices fluctuate with interest rates; selling before maturity may result in a gain or loss relative to the purchase price. This calculator is for educational and analytical purposes only and does not constitute investment advice.

Conclusion

YTM provides the apples-to-apples comparison metric for bonds with different coupons, prices, and maturities. After computing YTM on individual bonds, use the Portfolio Rebalancing Calculator to evaluate how your fixed income allocation fits your overall target. For the complementary calculation -- projecting the future value of bond-based retirement assets -- the Safe Withdrawal Rate Calculator incorporates bond portfolio returns into long-term retirement income modeling.