https://www.investopedia.com/terms/y/yieldtomaturity.asp
Investopedia / Jessica Olah
Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate. In other words, it is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity, with all payments made as scheduled and reinvested at the same rate.
Yield to maturity is also referred to as "book yield" or "redemption yield."
Yield to maturity is similar to current yield, which divides annual cash inflows from a bond by the market price of that bond to determine how much money one would make by buying a bond and holding it for one year. Yet, unlike current yield, YTM accounts for the present value of a bond's future coupon payments. In other words, it factors in the time value of money, whereas a simple current yield calculation does not. As such, it is often considered a more thorough means of calculating the return from a bond.
The YTM of a discount bond that does not pay a coupon is a good starting place in order to understand some of the more complex issues with coupon bonds.
The formula to calculate YTM of a discount bond is as follows:
\begin{aligned} &YTM=\sqrt[n]{\frac{\textit{Face Value}}{\textit{Current Price}}}-1\\ &\textbf{where:}\\ &n=\text{number of years to maturity}\\ &\text{Face value}=\text{bond's maturity value or par value}\\ &\text{Current price}=\text{the bond's price today} \end{aligned}
Because YTM is the interest rate an investor would earn by reinvesting every coupon payment from the bond at a constant interest rate until the bond's maturity date, the present value of all the future cash flows equals the bond's market price. An investor knows the current bond price, its coupon payments, and its maturity value, but the discount rate cannot be calculated directly. However, there is a trial-and-error method for finding YTM with the following present value formula:
Or this formula: