Bond YTM Calculator — Yield to Maturity
Solve for the yield to maturity (YTM) of a coupon bond — the single discount rate that equates all future cash flows to today's market price — using exact numerical iteration.
% p.a.
years
Coupon frequency
Discount bond — YTM > coupon rate
How does this calculator work?
YTM is the discount rate r that equates all future coupon payments and the face-value redemption to today's bond price. It is solved iteratively from P = C × [1−(1+r)^−n]/r + FV(1+r)^−n. Enter face value, coupon rate, current price, maturity and payment frequency to get the exact YTM and the convex price-yield curve.
Formula
How this is calculated
Yield to maturity is the internal rate of return of a bond held to maturity: it is the discount rate r that satisfies P = Σ C/(1+r)^t + FV/(1+r)^n, where C is the periodic coupon, n the total number of periods, and FV the face value. There is no closed-form algebraic solution for r, so this calculator uses Newton-Raphson iteration starting from the standard approximation YTM ≈ [C + (FV − P)/n] / [(FV + P)/2] and refining until the computed price matches the input price to within a penny.
The price-yield curve shown is the convex relationship between market yield and price: as yields rise, prices fall, but at a decreasing rate — this property is called positive convexity and means bondholders benefit more from falling yields than they suffer from equal yield increases. The current position of your bond on that curve is marked.
Assumptions: no default risk; coupon payments are reinvested at the same YTM (a simplifying assumption — actual reinvestment rates will differ); settlement is on a coupon date (no accrued interest). For bonds trading between coupon dates, professional platforms add accrued interest to the clean price. YTM is an annual figure here; the internal periodic yield is YTM / frequency.
Frequently asked questions
Current yield is just annual coupon divided by price — it ignores capital gain or loss at maturity. YTM accounts for all cash flows (coupons + face value repayment) and the time value of money, making it the most complete single measure of bond return if held to maturity.
The present-value formula implicitly assumes each coupon is reinvested and compounds at the same discount rate r. In practice, reinvestment rates will differ. When actual reinvestment rates fall short of YTM, the realized return will be lower than YTM — a risk called reinvestment risk.
The algorithm may not converge if inputs are economically implausible — for example, if the coupon rate is 0 and the bond trades at a huge premium, or the maturity is very short. Verify that face value, price and coupon are reasonable for a real bond.
TG we-Calculate Editorial Team. (2026). Bond YTM Calculator — Yield to Maturity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/bond-ytm-calculator
TG we-Calculate Editorial Team. "Bond YTM Calculator — Yield to Maturity." TG we-Calculate. 2026. https://we-calculate.com/calculator/bond-ytm-calculator.
TG we-Calculate Editorial Team, "Bond YTM Calculator — Yield to Maturity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/bond-ytm-calculator
@misc{wecalculate_bond_ytm_calculator, title = {Bond YTM Calculator — Yield to Maturity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/bond-ytm-calculator}}, year = {2026}, note = {TG we-Calculate} }
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