Bond Yield Calculator
Compute a bond's true yield to maturity rather than its coupon or its current yield — and see how far the price falls when rates move against you.
Bond Yield Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Results are a model, not a quotation — an institution's own figures govern.
- Every input is an assumption; change one and the answer changes with it.
- Rounding is applied only at the display layer, so totals may differ by a cent from a statement that rounds each line.
In short: A $1,000 bond with a 4.5% coupon bought at $920 with eight years remaining yields 5.762% to maturity, not the 4.5% coupon nor the 4.891% current yield. The difference is the $80 discount amortising to par. Its modified duration of 6.56 means a 100 basis point rise in yields would cut the price by $58.03.
Formula
P = price · C = coupon per period · F = face value · n = periods. There is no closed form, so the yield is recovered numerically.
Worked Example
- Size the coupon. $1,000 × 4.5% ÷ 2 = $22.50 every six months, sixteen times.
- Compute the current yield. $45 ÷ $920 = 4.891% — better than the coupon, because you paid less than par.
- Discount every cash flow. Find the rate at which sixteen coupons plus $1,000 at maturity are worth exactly $920 today.
- Annualise it. The per-period rate is 2.8811%, so the yield to maturity is 5.762%.
- Measure the rate risk. Modified duration of 6.56 implies a 100bp rise costs roughly 6.56% of the price — the exact repricing is $58.03.
Analyst's note. Three different yields describe this one bond: the 4.5% coupon, the 4.891% current yield, and the 5.762% yield to maturity. Only the last is a return, because only it counts the $80 discount that accretes to par over eight years. Note too that the popular textbook approximation gives 5.729% — 3.3 basis points light, which on an institutional position is real money.
Strengths & Limits Of This Model
Where this engine is strong
- Runs entirely in your browser — no figure you type is transmitted or stored.
- Shows the full working, so every number can be traced and challenged.
- Free, unmetered and free of affiliate incentives.
Where it stops
- Generalised assumptions cannot capture every individual circumstance.
- Jurisdiction-specific rules and mid-year changes may not be reflected.
- A model output is not a substitute for a professional review of your position.
Practical Use Cases
Comparing bonds trading at different prices
Coupon rates are not comparable across bonds bought at different prices. Yield to maturity is, because it folds the discount or premium into the return. Compare the result against a risk-free benchmark using the Treasury Yield Calculator to see what you are being paid for the credit risk.
Sizing your exposure to a rate move
Duration is the single most useful risk number in fixed income. A modified duration of 6.56 means a one-point rise in yields costs about 6.56% of capital. Test the actual repricing with the shock field before buying a long-dated bond in a rising-rate environment.
Deciding between a bond and a deposit
A bond's yield is only comparable with a deposit rate once both are expressed on the same basis. Convert the deposit to its effective annual yield with the APY Calculator, then weigh the extra yield against the credit and rate risk a bond carries.
Methodology & Editorial Standards
Yield to maturity is found by bisection on the per-period discount rate over 300 iterations, which converges far beyond display precision and cannot diverge near the boundary as Newton-Raphson can. It is annualised by multiplying by the coupon frequency, following the bond-equivalent convention used in US markets; the compounded effective annual yield is shown alongside because the two are routinely confused. Duration is computed as Macaulay duration from the same discounted cash flows and converted to modified duration by dividing by one plus the periodic yield. The price shock is a full repricing at the new yield, not a duration approximation, so it captures convexity. Accrued interest, settlement conventions, call features, credit risk and taxes are not modelled. The engine implements the standard published formula for this calculation. Inputs are validated for domain and sign before evaluation, and any undefined case returns an em-dash rather than a spurious value.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Bond Yield Calculator — 20 Expert FAQs
20 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is the difference between coupon, current yield and YTM?
The coupon is a fixed percentage of face value. The current yield divides the annual coupon by the price you actually paid. Yield to maturity additionally amortises the discount or premium over the remaining life — 4.5%, 4.891% and 5.762% respectively here.
Why is my yield higher than the coupon?
Because you bought below par. The $80 discount is returned to you at maturity when the bond redeems at $1,000, and spreading that gain across eight years lifts the effective return above the coupon rate.
How is yield to maturity calculated?
By finding the discount rate at which all future coupons plus the redemption value equal today's price. There is no algebraic solution, so it is solved numerically — this engine uses 300 bisections on the per-period rate.
What is duration and why does it matter?
Modified duration estimates the percentage price change for a one-point move in yields. At 6.56 here, a 100bp rise costs roughly 6.56% of the price. It is the standard measure of interest-rate risk and it rises with maturity and falls with coupon.
What happens to bond prices when rates rise?
They fall, because newly issued bonds offer better coupons and existing bonds must reprice to compete. On these figures a one-point rise takes the price from $920 to $861.97 — a $58.03 loss on an investment many people consider safe.
Is the textbook YTM approximation good enough?
For mental arithmetic, usually. The common formula gives 5.729% against the true 5.762% — 3.3 basis points out. On a retail holding that is negligible; on an institutional book it is not, which is why this engine solves it properly.
What is the effective annual yield?
The yield compounded rather than simply annualised. A 2.8811% semi-annual rate is 5.762% by convention but 5.845% when compounded. US markets quote the former, so compare bonds on that basis and deposits on the latter.
Does YTM assume I reinvest the coupons?
Yes, implicitly at the YTM itself — which is its main weakness. If you spend the coupons or reinvest at lower rates, your realised return will be below the quoted yield. This is reinvestment risk.
What if the bond is callable?
Then yield to call may matter more than yield to maturity, because the issuer will redeem early if rates fall. Callable bonds should be assessed at yield to worst — the lower of the two. This engine prices to maturity only.
Why does a longer maturity mean more risk?
Because more cash flows are discounted over longer periods, so duration is higher and prices move more for a given yield change. A 30-year bond can lose several times as much as an 8-year bond on the same rate move.
Are bond returns taxed?
Coupons are generally taxed as income, and any gain from buying at a discount may be taxed as income or capital gain depending on jurisdiction and the size of the discount. US Treasuries are exempt from state tax; municipals may be exempt federally.
What is accrued interest?
The coupon earned since the last payment date, which a buyer pays to the seller on top of the quoted price. This engine works from a clean price, so add accrued interest separately when reconciling with a broker's settlement figure.
Can yield to maturity be negative?
Yes, when a bond's price exceeds the total of all remaining cash flows — which happened widely in Europe and Japan during the negative-rate period. This engine solves for non-negative yields only.
What does trading at a premium mean?
The price exceeds face value, usually because the coupon is above prevailing market rates. The premium erodes to zero by maturity, so the yield to maturity is below the coupon rate — the mirror image of this example.
How does credit risk affect yield?
Riskier issuers must offer higher yields to compensate for default probability. A corporate bond yielding materially more than a Treasury of the same maturity is not free money; the spread is the market's price for that risk.
Is this bond yield calculator free to use?
Yes. It is free, requires no account, and has no usage limits. ApexConverter is funded by contextual advertising, never by selling user data.
Is my data sent to a server?
No. The engine runs as Vanilla JavaScript inside your browser under our Zero-Server Client-Side Execution model. Your figures are computed locally and are never transmitted, logged, or stored.
How accurate is this calculator?
It applies the standard closed-form formula in IEEE-754 double precision, rounding only at the display layer. The engine is reconciled against an independent reference implementation before release.
Does it work on mobile?
Yes. The interface is mobile-first with numeric keypad hints and is tested down to a 320-pixel viewport with no horizontal scrolling.
Can I use it offline?
Largely, yes. Because computation is client-side, the page continues to calculate without a network connection once it has loaded.