Consider the 4.625 bond maturing 8/15/2023 quoted in the following table (settlement: 2/15/2022).

Assume you purchase the bond on 2/15/2022, and you sell it on 8/15/2023. Let y denote the yield to maturity on the bond at the time of purchase.

In this case, why the yield to maturity(ytm) on the bond at the time of purchase is 4.17%? how to calculate ytm?

\begin{tabular}{ccc} Rate & Maturity & Price \\ \hline 687 & 8/15/2022 & 101:20 \end{tabular} 5214852/15/20238/15/2023101:18100:21