Bond Price & Yield Calculator

Yield to maturity (YTM) is the total annualized return you'd earn if you bought a bond at its current market price and held it until maturity, reinvesting every coupon at the same rate. It accounts for the coupon income and any capital gain or loss from buying above or below par.

The coupon rate, on the other hand, is simply the annual interest payment expressed as a percentage of the face value. It never changes — it's set when the bond is issued.

How they compare:

• Coupon rate — Fixed at issuance. A bond with a $1,000 face value and a 5% coupon pays $50 per year, regardless of what happens to its market price.
• Current yield — Annual coupon divided by the current market price. If that 5% coupon bond trades at $950, the current yield is $50 / $950 = 5.26%. This captures income but ignores capital gains.
• YTM — The full picture. It factors in coupon income, the difference between purchase price and par value, and time to maturity. It's the bond's true "all-in" return if held to maturity.

When does YTM differ from the coupon rate? Whenever the bond trades away from par. If you buy a 5% coupon bond at $950 (a discount), your YTM will be higher than 5% because you also profit from the $50 price appreciation as the bond matures back to $1,000. If you buy at $1,050 (a premium), your YTM will be lower than 5% because you absorb a $50 loss at maturity.

Current yield is the simplest income measure for a bond:

Current Yield = Annual Coupon Payment / Current Market Price

For example, a bond with a $50 annual coupon trading at $980 has a current yield of $50 / $980 = 5.10%. It tells you the income return you're getting right now, relative to what you paid.

When current yield is useful:

• Income-focused investors — If your primary goal is regular cash flow (e.g., retirees living off bond interest), current yield tells you what percentage of your investment comes back as income each year.
• Quick comparisons — It's easy to calculate and useful for a rough comparison between bonds with similar maturities.

When current yield falls short:

• It ignores capital gains or losses from buying above or below par
• It doesn't account for the time value of money
• It can be misleading for bonds trading far from par or with very short/long maturities

For a complete picture of what a bond will return over its full life, YTM is the better measure. But current yield remains a handy shorthand for the income stream a bond provides.

Macaulay duration measures the weighted average time it takes to receive a bond's total cash flows, where each cash flow is weighted by its present value. It's expressed in years and tells you how sensitive a bond's price is to changes in interest rates.

The formula:

Duration = [Σ (t × PV(CF_t))] / Price

In plain English: you take each cash flow, multiply it by when it occurs (year 1, year 2, etc.), discount it to present value, sum them all up, and divide by the bond's price.

Why duration matters:

• Interest rate risk — A bond with a duration of 7 years will lose approximately 7% of its price for every 1% increase in interest rates. The higher the duration, the more sensitive the bond is to rate changes.
• Portfolio management — Fund managers use duration to match the interest rate sensitivity of their assets to their liabilities. This is called duration matching or immunization.
• Bond comparison — Two bonds might have the same maturity but very different durations. A zero-coupon bond has duration equal to its maturity, while a high-coupon bond has a shorter duration because you receive more cash flow earlier.

Key factors that affect duration:

• Maturity — Longer maturity = higher duration
• Coupon rate — Higher coupon = lower duration (you get more cash back sooner)
• Yield — Higher yield = lower duration (distant cash flows are discounted more heavily)

Think of duration as a bond's "interest rate speedometer." The higher it is, the faster the bond's price moves when rates change — in either direction.

The inverse relationship between bond prices and yields is one of the most fundamental concepts in fixed income. It comes directly from the math of present value.

Here's the intuition: A bond promises fixed cash flows (coupons + face value). When market interest rates rise, new bonds are issued with higher coupons. Your existing bond, with its lower coupon, becomes less attractive by comparison — so its price must fall until its yield matches the new market rate.

Mathematically: Bond price is a sum of discounted cash flows. When you increase the discount rate (yield), the present value of each future cash flow decreases, pulling the total price down. When you decrease the yield, the present value of each cash flow rises, pushing the price up.

A concrete example:

• A 10-year, 5% coupon bond priced at yield 5% = $1,000 (par)
• Same bond at yield 6% = approximately $926 (price drops)
• Same bond at yield 4% = approximately $1,081 (price rises)

This is why bond investors watch Federal Reserve decisions so closely. When the Fed raises rates, existing bond prices decline. When rates are cut, bond prices rally. The price sensitivity chart in this calculator visualizes this relationship across a range of yields so you can see exactly how much a rate change would affect your bond's value.

A bond is classified by where its market price sits relative to its face (par) value — and this classification tells you a lot about the relationship between its coupon rate and the prevailing market yield.

Premium bond (price > par):

• The bond's coupon rate is higher than the current market yield
• Investors pay extra for the above-market coupon income
• The premium gradually declines as the bond approaches maturity (this is called amortization of the premium)
• YTM will be lower than the coupon rate because the investor loses money on the price decline to par

Discount bond (price < par):

• The bond's coupon rate is lower than the current market yield
• The discount compensates for below-market coupon payments
• The discount narrows as maturity approaches (called accretion of the discount)
• YTM will be higher than the coupon rate because the investor gains from the price appreciation to par

Par bond (price = par): The coupon rate equals the market yield. There's no premium or discount, and the YTM equals the coupon rate.

Practical note: Buying a premium bond isn't "overpaying" — the higher coupons compensate you. Similarly, a discount bond isn't a "bargain" — the lower coupons reflect the market rate. What matters is the YTM, which accounts for both the income and the price change.

Coupon bonds pay periodic interest (usually semi-annually or annually) throughout their life, then return the face value at maturity. Zero-coupon bonds pay no interest along the way — they're sold at a deep discount and return the full face value at maturity. Your entire return comes from the price appreciation.

Key differences:

• Cash flow pattern — Coupon bonds provide regular income; zero-coupon bonds provide a single lump sum at the end
• Price volatility — Zero-coupon bonds have higher duration (equal to their maturity) and are therefore more sensitive to interest rate changes
• Reinvestment risk — Coupon bonds carry reinvestment risk (you might have to reinvest coupons at lower rates); zero-coupon bonds eliminate this risk entirely
• Tax treatment — Zero-coupon bonds create "phantom income" — you owe tax on the imputed interest each year even though you don't receive any cash until maturity

Pricing a zero-coupon bond is simpler than a coupon bond because there's only one cash flow to discount:

Price = Face Value / (1 + r)ⁿ

For this calculator, if you set the coupon rate to 0%, you're effectively pricing a zero-coupon bond. The duration will equal the maturity, and the entire return will come from the difference between the purchase price and the face value.

Bond yields and DCF discount rates are deeply connected. The yield on a government bond (like the 10-year U.S. Treasury) serves as the risk-free rate — the foundational building block for virtually every discount rate used in equity valuation.

The connection chain:

• Risk-free rate — Set by government bond yields. This is the return you can earn with essentially zero default risk.
• Cost of equity (CAPM) = Risk-free rate + Beta × Equity risk premium. Bond yields directly determine the baseline of this formula.
• WACC — Blends the cost of equity and after-tax cost of debt. Both components are influenced by the level of bond yields in the market.
• DCF valuation — Uses WACC to discount future free cash flows. When bond yields rise, WACC rises, discount rates go up, and stock valuations fall (all else equal).

Why this matters for stock investors: When the 10-year Treasury yields 5%, stocks need to offer a meaningfully higher expected return to justify the extra risk. When the 10-year yields 2%, the bar is lower, and investors are willing to pay higher multiples for equities. This is the mechanism through which bond markets influence stock prices.

Understanding bond pricing helps you become a better equity analyst because you understand the discount rate that drives every DCF model. The yield you calculate here is the same concept that gets plugged into the "r" in every present value formula.