Yield to Maturity (YTM) is the annualized return percentage that an investor would earn if the investor purchases a bond at its current market price and holds it until maturity. Essentially, it represents the internal rate of return (IRR) of the investment. For a regularly paying bond, YTM can be found using the following formula:
$$P \mmlToken{mo}[linebreak="auto"]{=}\left(\sum_{i=1}^{t}\frac {F\times r_{i}}{(1+YTM)^{i}}\right)+ \frac{F}{(1+YTM)^t}$$
t— number of periods;
ri— interest rate for period i;
Σ— the Greek uppercase letter sigma denotes the sum in mathematics (in this case, the sum of terms).
For a zero-coupon bond, YTM can be calculated using:
$$YTM \mmlToken{mo}[linebreak="auto"]{=}\sqrt[t]{\frac{F}{P}}-1$$
It's important to note that there is an inverse relationship between the market price of a bond and its yield to maturity — as the market price increases, the yield to maturity decreases, and vice versa.