The income this bond pays each year. Every year pays the coupon; the final year also returns the face value. Long maturities are sampled to keep the table readable.
Year
Coupon
Principal returned
Total cash flow
Year 1
$50
$0
$50
Year 2
$50
$0
$50
Year 3
$50
$0
$50
Year 4
$50
$0
$50
Year 5
$50
$0
$50
Year 6
$50
$0
$50
Year 7
$50
$0
$50
Year 8
$50
$0
$50
Year 9
$50
$0
$50
Year 10
$50
$1,000
$1,050
Estimates only — not financial, tax, or professional advice.
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What it calculates: Yield to Maturity (YTM), Current Yield, YTM by the Textbook Shortcut, Annual Coupon Income.
This bond quotes 5%, yields 5.263%, and returns 5.669% — all three are correct
A $1,000 bond with a 5% coupon pays $50 a year, fixed, for as long as you hold it. Buy it at face value and your return is 5%. Buy it at $950, as the default scenario does, and that same $50 is 5.263% of what you actually paid — the current yield. Hold it to maturity and you also collect the $50 discount back when the issuer redeems at par, which lifts the total return to 5.669%. Yield to maturity is the only one of the three that counts both the income and that final repayment.
Price = Σ C/(1+y)^t + F/(1+y)^n, solved for y | Current Yield = C/P
This is why bond prices move inversely to rates. The $50 coupon cannot change, so when market rates rise the only way a buyer gets a competitive return is to pay less for the bond. The price falls until the yield to maturity matches what is available elsewhere.
The textbook shortcut reads 5.641% against a true 5.669%, and on other bonds it is far worse
Most calculators report the approximation (C + (F − P)/n) ÷ ((F + P)/2), which spreads the discount evenly across the years instead of discounting each cash flow properly. On this bond it returns 5.641%, about three basis points light. That looks harmless until the inputs move.
On a thirty-year bond bought at $950 with a 12% coupon the shortcut reads 12.479% against a true 12.651%. It is not merely low — it has fallen below the current yield of 12.632%, which a genuine yield to maturity on a discount bond can never do. On a one-year bond trading at 55% of face the shortcut understates the yield by more than twenty percentage points. This tool solves for the rate that discounts every coupon plus the redemption back to the price you paid, by bisection, and reports the shortcut beside it so you can see the size of the error rather than take the claim on trust.
Below par the yield beats the coupon; above par it must fall short of it
A bond trading at a discount always yields more than its coupon rate, and a bond trading at a premium always yields less. The logic is arithmetic rather than sentiment: at $950 you receive $50 of income on $950 of outlay and a further $50 at redemption, so both components push the return above 5%. At $1,100 you receive $50 on $1,100 and then lose $100 at redemption, so both pull it below.
The size of the discount usually tells you what changed. A bond issued at 5% now trading at $950 is telling you that rates on comparable new issues have risen. A bond trading well below par with a very high coupon is usually saying something different — that the market doubts the issuer will pay at all, in which case the quoted yield is compensation for credit risk rather than a return you should expect to collect.
Collecting 5.669% requires reinvesting each $50 coupon at 5.669%, which almost never happens
Yield to maturity is an internal rate of return, and every internal rate of return assumes intermediate cash flows are reinvested at that same rate. Take the $50 coupon each year and spend it, or park it in a 2% account, and your realised return over the decade will be below the 5.669% the tool reports. Only a zero-coupon bond, which pays nothing until maturity, is free of this assumption.
It matters most on long bonds with large coupons, where reinvested income makes up a substantial share of the total. For a short bond or a low coupon, the gap between the quoted yield and what you actually realise is small. This is the main reason a portfolio’s realised return can trail the average yield to maturity of the bonds inside it.
Annual coupons, no call provision, and no credit risk
The model pays one coupon a year and redeems at maturity. Most corporate and government bonds pay semi-annually and are quoted on a bond-equivalent basis, which will differ modestly from the figure here. It also assumes maturity is certain: a callable bond can be redeemed early by the issuer, usually exactly when rates have fallen and you would least like your money back, and for those the yield to call often matters more than the yield to maturity.
Nothing here models default. A yield is only a return if the issuer pays, and the spread between a corporate bond and a government bond of the same maturity is largely the market’s price for that risk. Accrued interest between coupon dates, taxes, and dealer spreads are all outside the calculation too — for anything you are actually buying, check the quoted yield on the confirmation.
Frequently Asked Questions
What is yield to maturity?
Yield to maturity (YTM) is the total annual return you would earn if you buy a bond at its current price and hold it until it matures. It blends the coupon income with any gain or loss from buying below or above face value. Because it accounts for both, YTM is the most complete single measure of a bond’s return.
What is the difference between coupon rate, current yield, and YTM?
The coupon rate is fixed and set against face value, so a 5% coupon on a $1,000 bond always pays $50 a year. Current yield divides that coupon by the price you actually paid, so it rises when the price falls. YTM goes one step further and also folds in the gain or loss you realise when the bond matures at face value.
What does buying a bond at a discount or premium mean?
A discount means the price is below face value, which happens when the coupon is lower than current market rates; the YTM ends up above the coupon rate. A premium means the price is above face value, which happens when the coupon is higher than market rates; the YTM ends up below the coupon rate. A bond priced at face value is said to trade 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 less becomes less attractive, so its price drops until its yield matches the market. The reverse happens when rates fall. This inverse relationship between price and yield is one of the core ideas in fixed income.
Does YTM assume I reinvest the coupons?
Yes. The classic YTM figure assumes every coupon is reinvested at the same yield until maturity. In practice you might reinvest at higher or lower rates, so the return you actually realise can differ. This gap is known as reinvestment risk and matters more for long-dated, high-coupon bonds.
What is the main risk of holding a bond to maturity?
If you hold to maturity and the issuer does not default, you receive the coupons and face value as scheduled, so price swings along the way do not affect your final outcome. The two risks that remain are credit risk, the chance the issuer cannot pay, and reinvestment risk on the coupons. Selling before maturity adds interest-rate risk, since the price you get depends on rates at that moment.
How do investors use these yields together?
Current yield gives a quick read on the income relative to today’s price, which is useful if you mainly care about cash flow. YTM is the better number for comparing bonds of different prices and maturities on a like-for-like basis. Most investors glance at the coupon for the income, then lean on YTM to judge whether a bond is fairly priced.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Annual coupon payments, with the redemption paid at maturity.
YTM is solved exactly by bisection; the shortcut figure is shown only for comparison.
Coupons are assumed reinvested at the YTM itself, which is what any YTM figure means.
Where it stops
Assumes annual coupons; a semi-annual bond quoted on a bond-equivalent basis will differ.
The shortcut figure is shown for comparison only — within 15% of par it is inside a tenth of a point about 62% of the time and can be a full point out at a high coupon over a long maturity, and it is increasingly wrong outside that band, by 30 percentage points on a short, deeply discounted bond.
Does not account for callable or puttable bonds, where yield to call can matter more than yield to maturity.
Assumes every coupon is reinvested at the YTM, which real reinvestment rates rarely match.
Ignores taxes, accrued interest between coupon dates, and any credit risk of the issuer.
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Published the calculator with its formula, worked example, assumptions, limitations and FAQs, and added an automated formula test suite covering it.
Replaced the textbook approximate yield to maturity with an exact solve by bisection, after testing showed the shortcut could understate the yield by more than 20 percentage points on a short, deeply discounted bond and could even print a yield below the current yield, which a true YTM on a discount bond never does. The shortcut is now shown as a separate, labelled line so its error is visible, and the worked example, methodology and FAQ were corrected — they had previously claimed the exact yield would be lower than the approximation when it is higher.
Frequently Asked Questions now show on the page: 7 answers, checked in a page-by-page audit.
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