When you buy a bond, the coupon rate printed on the security almost never tells you how much you will actually earn. If you pay less than its face value (at a discount) or more (at a premium), your effective return will differ from the coupon. The measure that puts it all together — coupons, price paid and capital gain or loss at maturity — is the yield to maturity (YTM). The yield to maturity calculator solves the equation for you (which has no closed-form formula) and tells you the real annual return you will get if you hold the bond to redemption, comparing it with the coupon and the current yield.

What yield to maturity (YTM) is

The yield to maturity is the total annual rate of return you will get from a bond if you buy it today at the market price and hold it to maturity, collecting all the coupons and the redemption of the face value. Technically it is the internal rate of return of the bond's cash flows: the discount rate that makes the present value of all future coupons plus the final redemption exactly equal to the price you pay today. It is the only measure that simultaneously accounts for three things: the coupon income, the price paid relative to the face value and the time left to maturity. That is why it is the standard measure with which investors compare different bonds: two securities with the same coupon but different prices have different YTMs, and two securities with different coupons can have the same YTM.

YTM, coupon and current yield: the differences

Three numbers are often confused. The coupon rate is the percentage, fixed at issue, that the issuer pays on the face value: a 1,000 bond with a 5% coupon pays 50 a year, always, regardless of the market price. The current yield is the annual coupon divided by the price you pay: if you buy that same bond at 950, the current yield is 50/950 = 5.26%. The yield to maturity adds the last piece: the gain (or loss) in capital when the bond is redeemed at 1,000 versus the 950 you paid. YTM is therefore the most complete measure: the current yield ignores the capital, the coupon rate ignores the price. Only YTM puts them together.

How YTM is calculated

Unlike the current yield, YTM has no closed-form formula: it appears as an exponent in every term of the price equation and cannot be isolated algebraically. It is found by numerical iteration: you try a rate, compute the present value of the flows, compare it to the price and adjust until they match. The calculator uses the bisection method: because the present value falls when the rate rises, it progressively narrows the yield interval until it finds the rate that exactly reproduces the price paid. It is the very same calculation done by financial calculators and professional terminals. You enter face value, price, coupon, years to maturity and coupon frequency; the calculator does the iterative work and returns the annual YTM.

Discount, par and premium bonds

The relationship between price and face value determines everything. If you buy below par (price lower than face, "at a discount"), in addition to the coupons you earn the difference at maturity: the YTM is higher than the coupon. If you buy at par (price equal to face), there is no capital gain or loss: the YTM coincides with the coupon. If you buy above par (price higher than face, "at a premium"), at maturity you receive less than you paid: the YTM is lower than the coupon. This is the key relationship to understand: a high coupon rate does not automatically mean a good deal, because you might pay the bond at a premium and see the real return fall below the coupon. The calculator immediately tells you which of the three cases you are in.

How YTM changes with price

Here is how the yield to maturity of a 1,000 face-value bond, 5% coupon and 10 years to maturity, varies as the purchase price changes:

For the same coupon, the lower the price you pay, the higher the yield: it is the heart of bond investing. The price you pay matters as much as the coupon.

The inverse link between price and yield

The previous table illustrates the fundamental law of bonds: price and yield move in opposite directions. When a bond's price falls, its yield rises; when the price rises, the yield falls. It is logical: the future flows (coupons and redemption) are fixed, so paying less for them means earning more in percentage terms. This inverse relationship also explains why the prices of already-issued bonds fall when market rates rise: if new bonds are issued with higher coupons, the old ones with a low coupon must fall in price until their YTM matches the new yields. Understanding this link is essential: the YTM you calculate today applies to today's price, and it will change if the market price changes before you buy.

Annual and semiannual coupons

Many bonds pay coupons more than once a year, typically every six months (semiannual). This affects the YTM because you receive the money sooner and can reinvest it. In the calculator you set the coupons per year: 1 for annual, 2 for semiannual (the most common on government and international corporate bonds), up to 12. The total annual coupon stays the same (a 5% coupon on 1,000 is 50 a year, whether paid in one or two installments), but with more frequent payments the annualized YTM is slightly different due to the time value of money. The calculator handles frequency correctly, discounting each single coupon in the right period and annualizing the yield. Use the real frequency of the security you are evaluating to get the correct YTM.

The capital gain or loss

Besides the coupons, a fundamental part of the return of a bond held to maturity is the capital gain or loss: the difference between the face value redeemed and the price paid. If you buy at 950 a security that will be redeemed at 1,000, you collect 50 of capital gain at maturity, in addition to the coupons. If you buy at 1,080, you suffer 80 of capital loss, which reduces the overall return below the coupon. The calculator shows this amount separately, so you see where your return comes from: how much from the coupons (income) and how much from the price difference (capital). In premium bonds, the capital loss can significantly erode the return, a detail that the coupon rate alone completely hides.

YTM by coupon and maturity

Here is the yield to maturity of a bond bought at 950 (discount) on a 1,000 face value, as the coupon and years to maturity vary:

Note two things: for the same discount, a shorter maturity gives a higher YTM (the capital gain is "spread" over fewer years), and higher coupons give higher YTMs. The YTM synthesizes both effects in a single comparable number.

Why YTM is the right measure to compare bonds

Imagine two bonds: one with a 6% coupon at a price of 1,100 and one with a 4% coupon at a price of 950, both at 10 years. Which yields more? The coupon rate would say the first, but after considering the price paid and the redemption at maturity the second might win. Only YTM makes them comparable, because it reduces the entire flow profile to a single annual rate. That is why bond markets think in terms of yield, not coupon: when you hear "the ten-year yields 4%," that 4% is a YTM. The calculator lets you compute the YTM of different securities and put them on the same footing, the most useful thing to decide where to invest in bonds.

The limits of YTM: the reinvestment assumption

YTM is powerful but rests on some assumptions to know. The main one: it assumes you hold the bond to maturity and that you reinvest every coupon at the same YTM rate. In reality, the coupons collected might be reinvested at different rates (higher or lower), so the actually realized return can diverge from the YTM: this is the so-called "reinvestment risk." Moreover, if you sell before maturity, your return will depend on the sale price, not on the YTM calculated today. YTM also assumes the issuer pays everything on time (no default). Despite these limits, it remains the best synthetic measure available: just remember it is a "theoretical yield to maturity," not a guarantee.

Interest rate, credit and reinvestment risk

YTM measures return, not risk. A high yield often signals high risk. Interest rate risk: if market rates rise, the price of your bond falls (and vice versa); the longer the maturity, the stronger this effect (the "duration"). Credit risk: if the issuer has a low rating, it offers a higher YTM to compensate for the default probability — a YTM far above average is not a free lunch, it is a premium for risk. Reinvestment risk: as seen, the realized return depends on the rates at which you reinvest the coupons. Comparing YTMs makes sense only among bonds of similar risk: a German government bond and a high-yield bond with the same YTM are not at all the same investment.

YTM compared with other indicators

Here are the main yield indicators of a bond, what they measure and their limits:

The coupon rate and current yield are useful for a quick glance, but only YTM captures the real return. For a serious comparison between bonds, YTM is the measure to use.

Negative yields: when and why

Can a bond have a negative yield to maturity? Yes, and it is not just theory: in recent years many high-quality government bonds traded at negative yields. It happens when the price is so high relative to the future flows that the sum of the coupons and the redemption is less than what you pay today: in practice, you guarantee to lose money in nominal terms if you hold the security to maturity. Why would anyone buy? For safety (parking capital in a very solid issuer), for regulatory obligations (banks and insurers), or betting that prices rise further. The calculator detects and flags negative yields: if you see it, it means you are paying too much for the bond relative to what it will return.

How the calculator works

Enter the face value (the redemption at maturity, often 100 or 1,000), the current purchase price, the annual coupon rate, the years to maturity and the number of coupons per year. The calculator solves the yield to maturity by iteration and returns the annual YTM, the current yield, the capital gain or loss and the annual coupon income, with an assessment of whether the security is at a discount, at par or at a premium. Try different prices to see the inverse price-yield link, or different maturities to understand the effect of time.

The data you need

You need five data, all on the security's fact sheet. The face value (or par value, the redemption at maturity). The current market price (caution: often quoted as a percentage of face, e.g. "95" means 950 on a 1,000 face value). The annual coupon rate. The years to maturity (or the maturity date to calculate them from). The coupons per year (1 annual, 2 semiannual). The result is the gross YTM, before taxes and fees, and assumes you hold the security to maturity reinvesting the coupons at the same rate: it is the standard market measure, not a guarantee of realized return.

A worked example

Consider a security with a face value of 1,000, an annual coupon of 5% (i.e. 50 a year), 10 years to maturity, bought today at 950. The current yield is 50/950 = 5.26%. But at maturity you will also collect 50 of capital gain (1,000 redeemed versus 950 paid), spread over ten years. Putting it all together, the yield to maturity is about 5.67%: above both the coupon (5%) and the current yield (5.26%), because you bought at a discount. If instead you had paid 1,080 for the same security (at a premium), the YTM would fall to about 4.1%, below the coupon, because at maturity you would recover only 1,000 against the 1,080 paid. Same security, same coupon: it is the price that decides the real return, and that is exactly what YTM captures and the coupon does not.

Frequently asked questions

What is yield to maturity (YTM)?

It is the total annual rate of return of a bond if you buy it today at the market price and hold it to maturity, collecting all coupons and the redemption of the face value. It is the internal rate of return of the flows: the discount rate that makes the present value of coupons and redemption equal to the price paid. It accounts together for coupon, price and time to maturity.

What is the difference between YTM, coupon and current yield?

The coupon rate is the coupon as % of face (fixed). The current yield is the annual coupon divided by the price (ignores the capital). The YTM adds the capital gain/loss at maturity and is the most complete measure. Example: face 1,000, coupon 5%, price 950 → coupon 5%, current 5.26%, YTM ~5.67%.

How is YTM calculated?

It has no closed-form formula: the rate appears as an exponent in every term and cannot be isolated. It is found by numerical iteration — you try a rate, compute the present value of the flows, compare it to the price and adjust until they match. The calculator uses bisection, the same method as professional financial calculators.

What does discount, par or premium bond mean?

Discount = price below face, the YTM is above the coupon (you earn the difference at maturity). Par = price equal to face, the YTM coincides with the coupon. Premium = price above face, the YTM is below the coupon (you lose the difference at maturity). It is the key relationship: a high coupon is not enough if you pay at a premium.

Why do price and yield move in opposite directions?

Because the future flows (coupons and redemption) are fixed: paying less for them means earning more in percentage terms. When the price falls the yield rises, and vice versa. It is also why the prices of already-issued bonds fall when market rates rise: they must adjust their YTM to the new yields.

What changes with semiannual coupons?

With more frequent payments you receive the money sooner and can reinvest it, so the annualized YTM is slightly different from annual coupons (due to the time value of money). In the calculator set the coupons per year: 1 annual, 2 semiannual (common on government and corporate bonds). The calculator discounts each coupon in the right period.

Is the YTM guaranteed?

No, it is a theoretical return based on assumptions: that you hold the security to maturity and reinvest every coupon at the same YTM rate. In reality reinvestment rates vary (reinvestment risk) and if you sell early the return depends on the sale price. It also assumes the issuer does not default. It remains the best synthetic measure, but not a guarantee.

Is a high YTM always a good deal?

No: a high yield often signals high risk. An issuer with a low rating offers a higher YTM to compensate for the default probability: it is a premium for risk, not a free lunch. Compare YTMs only among bonds of similar risk — a solid government bond and a high yield with the same YTM are not the same investment.

What is interest rate risk?

It is the risk that the price of your bond falls if market rates rise (and vice versa). The longer the maturity, the stronger the effect, measured by the "duration." It matters for those who might sell before maturity: if you hold to redemption you collect the face value, but meanwhile the market price fluctuates as rates change.

Can a bond have a negative yield?

Yes. It happens when the price is so high that the sum of coupons and redemption is less than what you pay: you guarantee a nominal loss by holding to maturity. It happened on many high-quality government bonds in recent years. People buy for safety, regulatory obligations or betting on further price rises. The calculator flags negative yields.

What data do I need for the calculation?

Five, all on the security fact sheet: face value (redemption at maturity), market price (often quoted as % of face, e.g. "95" = 950 on 1,000), annual coupon rate, years to maturity and coupons per year (1 annual, 2 semiannual). Be careful to correctly convert the price quoted as a percentage.

Is the result gross or net of taxes?

It is the gross YTM, before taxes and fees. The taxation of coupons and capital gains varies by country and security type, so the real net return will be lower. The calculator provides the standard market measure (gross), useful to compare securities with each other; for the net figure apply your country tax rules.

Is the calculator free?

Yes, it is completely free and without registration. You can compute the YTM of as many securities as you like, varying price, coupon, maturity and frequency, to compare them on the same footing and understand the price-yield relationship. It is an informational tool and is not an investment recommendation nor personalized financial advice.

Updated July 2026