Solve the coupon-date price for one yield
Yield to maturity is the single annualized rate that makes the present value of remaining coupons plus face equal the clean price, immediately after a coupon payment. US corporates and Treasuries usually pay twice a year; the solver finds the periodic rate and multiplies by payments per year. Bond price takes that yield as an input. Current yield is only annual coupon divided by price. This page solves the exact identity rather than the average-price shortcut.
Price = coupon annuity + face ÷ (1 + YTM ÷ payments per year)years × payments per year
Solve for YTM
Current yield = annual coupon ÷ price
Example
A $1,000 face bond with a 5% coupon, 10 years left, and semiannual payments trading at $950 has a 5.26% current yield. Exact coupon-date YTM is about 5.66%. The same bond at the $925.61 textbook price used on the bond-price page yields 6%. At a $1,000 price the yield equals the 5% coupon.
What this yield leaves out
Years and payments per year must be whole numbers. Accrued interest, settlement lag, call or put features, default risk, a term structure of spot rates, and day-count conventions stay outside this identity. A clean price above the 0% yield value implies a negative yield and is rejected. A price below the 100% yield value is also rejected. YTM is a model yield: realized return depends on timely payments, holding to maturity, and the rates available when coupons are reinvested.