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Yield to maturity is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the price of the bond. The YTM is often given in terms of Annual Percentage Rate (A.P.R.), but more usually market convention is followed.
The yield to maturity is found in the present value of a bond formula: For calculating yield to maturity, the price of the bond, or present value of the bond, is already known. Calculating YTM is working backwards from the present value of a bond formula and trying to determine what r is.