The bond pricing formula. A bond's price equals the present value of all future coupon payments plus the present value of face at maturity, discounted at the yield-to-maturity rate.
Price = Sum [t=1..n] (Coupon / (1 + y/m)^t) + Face / (1 + y/m)^n
Where:
Coupon = annual coupon ÷ m (periodic payment)y = yield to maturity (annual)m = payments per year (2 for semi-annual)n = total periods (years × m)
Current Yield — the simplest. Annual coupon divided by current price.
CY = (Coupon rate × Face) / Price
Yield to Maturity (YTM) — the IRR of the bond's cash flows. There is no closed-form solution; the tool uses Newton-Raphson iteration. Starting guess: current yield. Converges in <10 iterations for normal bonds.
Solve for y such that: Price − Sum(PV of coupons) − PV of face = 0
Yield to Call (YTC) — same calculation, but with the call price substituted for face and the years-to-call substituted for years-to-maturity. If a bond is trading above call price, the issuer is likely to call; YTC is the realistic yield in that case.
Yield to Worst (YTW) — the lower of YTM and YTC. That's what your broker quotes. This tool surfaces both so you can see which one binds.
After-Tax YTM. Couponseach period are taxed at your marginal ordinary-income rate (federal + state for taxable bonds; federal-only for Treasuries; tax-exempt for in-state munis; federal-exempt only for out-of-state munis). The tool re-runs the YTM solve with each coupon shrunk by the appropriate tax rate.
After-tax coupon = Coupon × (1 − t_eff)
Where t_eff depends on the bond type. Treasury interest is state-exempt by federal law (Public Salary Tax Act of 1939, codified at 31 USC 3124). In-state munis are typically federal + state exempt. Out-of-state munis are federal-exempt but state-taxable.