Bond yield calculator (current yield & YTM)

How the formula works

A bond is a stream of fixed payments: a coupon every period, and the face (par) value repaid once at maturity. Two yields describe what that stream is worth to you at today's price, and they answer different questions.

The current yield is the simplest: it divides the annual coupon in dollars by the price you pay, so it measures the cash income the bond throws off relative to its cost, and nothing else.

where \(F\) is the face value, \(c\) the coupon rate, and \(P\) the market price. The yield to maturity asks the harder question: what single rate makes every future payment, discounted back to today, add up to exactly the price? With \(N\) periods to maturity, a coupon of \(C = cF/m\) each period (\(m\) coupons a year) and the face \(F\) returned at the end, YTM is the periodic rate \(y\) solving

and the annualized figure the worksheet reports is \(y \times m\). There is no algebra that isolates \(y\) — the calculator finds it numerically, narrowing a bracket by bisection until the present value lands on the price.

Why YTM says more than current yield. Current yield counts only the coupon. YTM also counts the pull to par: if you buy a bond below its face value, you paid \(P\) but collect the full \(F\) at maturity, and that capital gain is part of your return — one that current yield ignores entirely. Buy above par and the reverse applies: a capital loss at maturity drags the true yield below the coupon. That is why the two figures split apart whenever the price is not par.

The price-yield relationship runs backwards. Read the YTM equation as a machine that turns a yield into a price and one fact falls out: raise \(y\) and every term shrinks, so the price falls; lower \(y\) and the price rises. Bond prices and market yields always move in opposite directions. When prevailing rates climb, an older bond's fixed coupon looks less generous, so its price must drop until its yield matches what new bonds offer — and vice versa. The relationship is also convex, curving rather than straight, which is why the figure below bows toward the origin.

What each input means

Face (par) value — \(F\)

The amount printed on the bond, repaid in full at maturity regardless of what you paid for it. Most corporate and Treasury bonds use $1,000. The coupon is a percentage of this figure, not of the price.

Coupon rate — \(c\)

The annual interest rate the bond promises, as a percent of face value. A 5% coupon on a $1,000 bond pays $50 a year, split across the coupon dates. It is fixed for the life of the bond and never changes with the market.

Current market price — \(P\)

What the bond trades for today. Below face is a discount, above face a premium. This is the quoted clean price; it is the only input that moves once the bond is issued, and every yield here is measured against it.

Years to maturity — \(N/m\)

How long until the face value is repaid and the coupons stop. Longer maturities give the pull-to-par gain or loss more time to matter, and make the price swing more for a given change in yield.

Coupons per year — \(m\)

How often the coupon is paid: semiannual (2) is the norm for U.S. bonds, with annual (1) and quarterly (4) also offered. It sets both the size of each coupon and the number of discounting periods, and the annualized YTM multiplies the solved periodic rate by this number.

A worked example

Take the worksheet's opening numbers: a $1,000 face bond with a 5% coupon, trading at $950, with 10 years left and semiannual coupons.

• The annual coupon is 5% of $1,000 = $50, paid as $25 every six months. The current yield is simply $50 / $950 = 5.26%.
• But you bought at a discount: you pay $950 today and are repaid $1,000 at maturity, a +$50 capital gain that the current yield never sees.
• Solving the price equation for the rate that discounts all 20 coupons plus the $1,000 face back to $950 gives a yield to maturity of 5.66% — above the 5% coupon, exactly because the pull to par adds to the return.
• Held to maturity the bond pays $500 in coupons plus the +$50 gain, a total return of $550 over the 10 years.

Assumptions and limits

• YTM assumes you hold the bond to maturity and reinvest every coupon at the YTM itself. If coupons are reinvested at a lower rate — the usual case when rates fall — your realized return comes in below the quoted YTM. This is reinvestment risk, and it is baked into the definition of YTM.
• It assumes the issuer pays in full and on time. Credit and default risk are ignored: a high yield often signals the market's doubt that the coupons and face will actually arrive, not a bargain.
• Call features are ignored. Many bonds can be redeemed early by the issuer, which caps the upside — for those, yield to call matters more than yield to maturity.
• Taxes, accrued interest and transaction costs are left out, and the price is the clean price (no accrued coupon). Municipal-bond interest is often tax-free, which changes how yields compare across bond types.
• This is arithmetic, not advice. It reports what the price and the coupons imply; it cannot judge whether the yield compensates for the risk.

Questions people ask

What's the difference between current yield and yield to maturity?

Current yield divides the annual coupon by the price, so it measures only the cash income relative to what you paid. Yield to maturity is the full return if you hold the bond to the end: it counts the coupons and the pull to par — the capital gain from buying below face value, or the loss from buying above it. On a discount bond YTM is higher than the current yield, which is higher than the coupon rate; on a premium bond the order reverses. They are equal only when the bond trades at par.

Why do bond prices fall when interest rates rise?

A bond's coupon is fixed for life. When new bonds are issued at higher rates, an older bond paying the old, lower coupon is worth less — nobody pays face value for a below-market income stream. Its price falls until its yield to maturity matches what the market now offers, so the discount makes up for the stingy coupon. The same logic in reverse lifts prices when rates fall. Price and yield are two ends of the same equation, and they always move in opposite directions.

What is yield to call?

Many bonds are callable: the issuer can repay them early, usually after rates have fallen and it wants to refinance cheaper. Yield to call runs the same present-value math as YTM but using the call date and call price instead of the maturity date and face value. Because a call typically happens when it hurts the holder, prudent buyers of a premium callable bond look at the yield to worst — the lower of yield to call and yield to maturity — rather than assuming the bond runs to term.

Can I compare Treasury, municipal and corporate yields directly?

Not at face value, because they are taxed differently. Treasury interest is exempt from state tax; municipal-bond interest is usually free of federal tax; corporate-bond interest is fully taxable. To compare a tax-free muni with a taxable bond, convert it to a tax-equivalent yield: divide the muni yield by (1 minus your marginal tax rate). A 3% muni is worth about 3.9% pre-tax to someone in the 24% bracket. Only after that adjustment are the yields comparable — and corporates also carry credit risk that Treasuries do not.

What does it mean for a bond to trade at a discount or a premium?

A bond trades at a discount when its price is below face value and at a premium when it is above. The cause is the gap between the fixed coupon and current market yields: a coupon below prevailing rates forces a discount, a coupon above them commands a premium. A discount bond hands you a capital gain at maturity, pushing yield to maturity above the coupon; a premium bond books a capital loss, pulling YTM below the coupon. Either way the price drifts toward face value as maturity nears — the pull to par.