Yield to Maturity Calculator

4 min read 3 steps 7 terms 3 examples 6 FAQs Price = Σ [C / (1 + y)^t] + F / (1 + y)^n

A bond's coupon rate only tells you what it pays — not what it actually returns to an investor who buys it today.

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Walk-through

How to Use This Calculator

3 steps

Enter the bond's details

Type the bond's current market price, its face (par) value, its stated annual coupon rate, and the number of years remaining until maturity. Choose how often it pays coupons — annual, semiannual, quarterly, or monthly.

Read the yield to maturity

The Yield to Maturity Calculator solves for YTM iteratively and updates instantly as you type. The result is the total annualized return the bond earns if held to maturity with coupons reinvested at that same rate.

Compare current yield and premium/discount

Switch to the Current Yield tab to see the simpler coupon-only yield, or the Premium/Discount tab to see how the price compares to face value and why that pushes YTM above or below the coupon rate.

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Reference

Formula & Methodology

2 formulas

Bond pricing equation (solved for yield)

Price = Σ [C / (1 + y)^t] + F / (1 + y)^n

C is the coupon payment per period, F is the face value, n is the total number of periods to maturity, and y is the yield per period. There is no closed-form algebraic solution for y when n > 1, so the calculator finds it iteratively — using Newton-Raphson with a bisection fallback — as the discount rate that makes the right-hand side equal the bond's current price. Multiply the periodic yield by the number of periods per year to get the annualized YTM.

Current yield

Current Yield = Annual Coupon / Price

A simpler, rougher measure than YTM: just the coupon income divided by what you paid. It ignores the capital gain or loss realized when the bond matures at face value.

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Trust, Methodology & Sources

Written by Calculover Editorial Team · Updated 2026-07-21 · 2 sources

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Author: {{^authorProfileUrl}}Calculover Editorial Team{{/authorProfileUrl}} - Finance content review

Owner: Calculover Editorial Team - Finance content review

Last reviewed: 2026-07-21

Last verified: 2026-07-21

Methodology

Yield to maturity is solved directly from the standard bond-pricing equation (Price = Σ C/(1+y)^t + F/(1+y)^n) using Newton-Raphson iteration with a bisection fallback for guaranteed convergence. YTM is annualized by multiplying the solved periodic yield by the number of coupon periods per year (Bond-Equivalent Yield convention). Current yield is computed directly as annual coupon divided by price.

Assumption: Coupon payments are assumed to occur at even intervals throughout the year based on the selected frequency, with the next payment exactly one period away.

Assumption: YTM assumes every coupon is reinvested at the same rate as the calculated yield — the standard textbook assumption, though actual reinvestment rates vary over time.

Assumption: The calculator relies on the values the user enters and does not independently verify issuer credit, settlement date, or live market quotes.

Limitations & guidance

This calculator does not model call provisions, credit or default risk, accrued interest between coupon dates, or tax treatment, all of which can change the return an investor actually realizes.

For callable bonds, duration/convexity analysis, or tax-equivalent yield, use the fuller Bond Yield Calculator instead.

Professional guidance: This calculator is for educational purposes only and does not constitute financial, tax, or investment advice. Consult a licensed financial advisor before making borrowing or investment decisions.

Primary sources

Compound Interest Calculator - Investor.gov

Introduction to Investing - Investor.gov

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Glossary

Key Terms Explained

7 terms

Yield to maturity (YTM) The total annualized return a bond earns if held until maturity and every coupon is reinvested at the same rate. It accounts for price, face value, coupon rate, and time remaining.

Bond price The amount the bond currently trades for in the market, which can be above, below, or equal to its face value depending on prevailing interest rates.

Face value Also called par value — the amount the issuer repays the bondholder at maturity, and the amount coupon payments are calculated against.

Coupon rate The bond's stated annual interest rate, expressed as a percent of face value. It determines the dollar amount of each coupon payment but does not change once the bond is issued.

Current yield Annual coupon payment divided by the bond's current price. Unlike YTM, it ignores any gain or loss from the price converging to face value at maturity.

Premium A bond trades at a premium when its price is above face value — typically because its coupon rate is higher than prevailing market rates. A premium bond's YTM is below its coupon rate.

Discount A bond trades at a discount when its price is below face value — typically because its coupon rate is lower than prevailing market rates. A discount bond's YTM is above its coupon rate.

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Scenarios

Real-World Examples

3 worked examples

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Discount bond

$1,000 face, 5% coupon, priced at $950, 10 years, semiannual

Price $950 Face value $1,000 Coupon rate 5% Years to maturity 10 Frequency Semiannual

YTM solves to approximately 5.66% — above the 5% coupon rate, because buying at $950 and collecting $1,000 at maturity adds a capital gain on top of the coupon income. Current yield is lower, at 5.26% ($50 coupon ÷ $950 price), since it ignores that gain.

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Current yield only

Same bond, coupon-only view

Annual coupon $50 (5% of $1,000) Price $950

Current yield = $50 ÷ $950 = 5.26%. This is quicker to compute than YTM but understates the true return on a discount bond, because it leaves out the $50 capital gain realized when the bond repays $1,000 at maturity.

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Premium bond

$1,000 face, 6% coupon, priced at $1,050, 10 years, semiannual

Price $1,050 Face value $1,000 Coupon rate 6% Years to maturity 10 Frequency Semiannual

YTM solves to approximately 5.35% — below the 6% coupon rate, because the extra $50 paid above face value is lost back at maturity. Current yield overstates the return here at 5.71% ($60 coupon ÷ $1,050 price), since it ignores that loss.

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Deep Dive

Understanding the Yield to Maturity Calculator

3 chapters · 4 min read

A bond's coupon rate only tells you what it pays — not what it actually returns to an investor who buys it today. The Yield to Maturity Calculator solves for the bond's true annualized return (YTM) from its price, face value, coupon rate, and time to maturity, and shows how that compares to the simpler current yield.

How the Yield to Maturity Calculator works

The calculator treats YTM as the single discount rate that, applied to every remaining coupon payment and the final face-value repayment, produces a present value equal to the bond's current price: Price = Σ C/(1+y)^t + F/(1+y)^n. Because this equation has no algebraic solution for a bond with more than one payment left, the calculator solves it numerically — Newton-Raphson iteration refines an initial guess (the current yield) toward the answer, with a bisection fallback that guarantees convergence even in edge cases where the derivative is unstable.

Inputs and what they mean

Price and face value are dollar amounts; coupon rate, current yield, and YTM are all annual percentages. Coupon frequency matters because it changes how often interest compounds — a bond with the same annual coupon rate but more frequent payments has a very slightly higher effective YTM. The default example (a $1,000 bond bought at $950 with a 5% coupon) is a typical discount scenario: YTM comes out above the coupon rate because the discount adds a capital gain on top of coupon income.

Limits and edge cases

This calculator computes the mathematical yield to maturity only. It does not model call provisions (use a dedicated yield-to-call calculation for callable bonds), credit or default risk, accrued interest between coupon dates, or tax treatment — all of which affect the return an investor actually realizes. For a fuller bond-analysis toolkit that covers duration, convexity, tax-equivalent yield, and callable bonds, see the Bond Yield Calculator. Consult a licensed financial advisor before making investment decisions based on this calculator alone.

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Questions

Frequently Asked Questions

6 questions

What is yield to maturity (YTM)?+

Yield to maturity is the total annualized return a bond earns if held until it matures and every coupon payment is reinvested at that same rate. It accounts for the coupon rate, the current price, the face value, and the time remaining, unlike current yield which only looks at coupon income against price.

How is YTM calculated?+

YTM has no closed-form algebraic solution for a bond with more than one coupon payment remaining, so this calculator solves for it iteratively (Newton-Raphson with a bisection fallback) by finding the discount rate that makes the present value of all future coupons plus the face value equal the bond's current price.

What is current yield and how does it differ from YTM?+

Current yield is simply the annual coupon payment divided by the bond's current price. It ignores the capital gain or loss you'll realize when the bond matures at face value, so it's a rougher estimate than YTM — current yield understates return on a discount bond and overstates it on a premium bond.

What does it mean when a bond trades at a discount?+

A bond trades at a discount when its market price is below its face value. This typically happens when the bond's coupon rate is lower than prevailing market interest rates. A discount bond's YTM is higher than its coupon rate, because you gain the difference between price and face value at maturity.

What units does the Yield to Maturity Calculator use?+

Bond price and face value are entered in dollars; the coupon rate, current yield, and yield to maturity are all expressed as a percent per year.

Why is YTM different from the coupon rate?+

YTM equals the coupon rate only when the bond trades exactly at par (price = face value). Whenever the market price differs from face value, YTM and the coupon rate diverge: YTM rises above the coupon rate for a discount bond and falls below it for a premium bond, because YTM also captures the capital gain or loss realized at maturity.

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