Yield to Maturity Calculator
Estimate a bond's yield to maturity (YTM) with the approximation formula, blending the coupon and the capital gain or loss to maturity into an annualised return.
Input Data
Results
At a glance:YTM is the annualised return of holding a bond to maturity. Annual coupon = face value × coupon rate%; approximate YTM = (annual coupon + (face value − price) ÷ years) ÷ ((face value + price) ÷ 2), as a percent. It mixes the coupon with the capital gain or loss to maturity. This is an approximation of the exact internal rate of return.
Formula
Annual coupon = face value × coupon rate%.
YTM ≈ (annual coupon + (face value − price) ÷ years) ÷ ((face value + price) ÷ 2) × 100.
$$C = \text{Face} \times \text{Coupon Rate}$$$$\text{YTM} \approx \dfrac{C + \dfrac{\text{Face} - \text{Price}}{n}}{\dfrac{\text{Face} + \text{Price}}{2}} \times 100\%$$How to Use
- Enter the face value, coupon rate, current price and years to maturity.
- Read the annual coupon and the approximate YTM.
FAQ
What is the difference between YTM, current yield and coupon rate?
These three describe bond return on a spectrum from narrow to wide. Coupon rate is narrowest: the fixed annual rate paid on face value, fixed at issue and unchanged, reflecting only the coupon base. Current yield is medium: annual coupon ÷ current market price (not face), reflecting the dividend return at today's price, but still counting only coupons, not the capital gain/loss to maturity. YTM is the most complete: it adds the capital gain/loss to maturity (buy at a discount earns the face-value spread, at a premium loses it) and annualises it. The ordering is regular: at a discount, YTM > current yield > coupon rate; at par, all three are equal; at a premium, YTM < current yield < coupon rate. So for comparing the 'true total return' of bonds, YTM is the one to watch; current yield is for a quick payout comparison; the coupon rate is only the basis for computing coupon amounts.
How accurate is this YTM—does it match the broker's quote?
This calculator uses an approximation formula that gives a close YTM quickly, but differs slightly from the broker's exact YTM solved by discounting cash flows; understand a few points. First, approximate vs exact: the exact YTM finds a discount rate that makes the present value of 'all future coupons + face at maturity' exactly equal the price—requiring iteration. This calculator's approximation linearly amortises the premium/discount over the years, simple but slightly more biased when price deviates far from face or the term is long (usually within a few tenths of a percent). Second, assumptions: the YTM concept itself assumes you hold to maturity and reinvest each coupon at the YTM—real reinvestment rates float, so the actual return may not exactly equal the YTM. Third, it ignores transaction costs and tax. So this tool is for quick estimation and comparison; for actual trading decisions, rely on the broker's exact YTM quote and weigh credit rating and liquidity.
Why is the YTM of a discount bond higher—does that make it better?
A discount bond (price below face) has a higher YTM because its return comes from two parts: the annual coupon, plus the capital gain at maturity (face − discount purchase price). YTM counts both and annualises them, so the deeper the discount, the higher the YTM sits above the coupon rate. Example: face HK$1,000, coupon 6%, 10 years, bought at HK$900 earns HK$100 on maturity plus HK$60 coupons, lifting YTM to about 7.37%. But 'high YTM' does not equal 'better or cheaper'—ask why the market sells it at a discount. Common reasons: the issuer's credit rating was cut and the market fears repayment (default risk rising); or market rates rose overall, forcing old low-coupon bonds to drop in price. The former is a risk premium—the high YTM compensates you for higher default risk, and if it defaults you may not even recover principal. So when you see a high YTM, check the issuer's credit rating and financials first to judge whether the return is worth the underlying risk, rather than simply chasing a high yield.
How do purchase price, coupon rate and years affect YTM?
YTM is mainly driven by three variables. First, purchase price (current price)—most direct and inverse: at fixed coupon and term, the lower the price (deeper discount), the higher the YTM; the higher the price (premium), the lower the YTM. For face HK$1,000, coupon 6%, 10 years: price HK$900 → YTM ≈ 7.37%, HK$1,000 → 6.00%, HK$1,100 → about 4.76%. Second, coupon rate—positive: the higher the coupon, the more annual cash flow, the higher the YTM (else equal). Third, years to maturity—affects the amortisation speed of the premium/discount: the approximation divides the (face − price) spread by the years, so with a premium/discount, a shorter term spreads the capital gain/loss over fewer years and pushes YTM more strongly; a longer term amortises it more gently and YTM moves closer to the current yield. Example: the same HK$100 discount spread over 5 years is HK$20 a year, over 20 years only HK$5, so the former lifts YTM more. Worth testing: fix a bond's face and coupon, compare YTM across different purchase prices and remaining terms, to assess whether the current market price offers an attractive maturity return.
How is YTM related to yield to call (YTC)—which to use for callable bonds?
YTM assumes you hold to maturity, but many corporate and some government bonds have a callable feature—the issuer may redeem early at an agreed call price on certain dates. For these, YTM alone is not enough; also look at YTC, which assumes redemption at the earliest call date and computes the annualised return to then. The relationship: issuers usually exercise the call when it benefits them—when rates fall and the bond rises to a premium, they call the old high-coupon bond and reissue cheaper, which is worst for you: you are forced to hand back the bond at a high price and lose future high coupons. So for callable bonds, prudently compute both YTM and YTC and use the lower of the two (yield to worst) as the conservative estimate. If a bond trades at a premium, YTC is often below YTM, so YTC should be your benchmark; at a discount, the issuer usually will not call, and YTM is more relevant. Pair this with our Yield to Call (YTC) calculator.
Related Tools
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.