The commonly used approximate yield-to-maturity formula is a shortcut — this calculator instead numerically solves for the actual, precise yield.
How it works
Since there’s no algebraic formula that isolates yield directly, this calculator searches by bisection (repeatedly narrowing a range) for the exact discount rate that makes the bond’s discounted cash flows equal its current price.
What this does not include
This does not include semi-annual compounding, which most U.S. bonds actually use — this calculator uses annual periods for simplicity, the same convention this site’s other bond-pricing calculators use.
How to use this calculator
- Enter the bond’s current price, face value, coupon rate, and years to maturity.
Frequently asked questions
How different is the exact YTM from the approximate formula?
Usually close but not identical — the gap grows larger the further a bond trades from its face value, since the approximation formula’s accuracy degrades with a bigger price-to-face-value gap.
Why doesn’t a simple algebraic formula exist for exact YTM?
Because the bond pricing equation involves the discount rate raised to different powers for each cash flow — a polynomial equation with no general closed-form solution for its roots beyond a couple of terms.
Is bisection the only way to solve this numerically?
No — Newton-Raphson and other root-finding methods can also solve it, often faster, but bisection is simple, robust, and guaranteed to converge as long as the answer is bracketed correctly.
