How to add class to anchor using wp_nav_menu

WordPress does in fact add a current class by default:

check where it says:

<li id="menu-item-1688" class="current-menu-item">

Within your source code.

Now as for the other item, this is a bit tricky.

There is two ways to do it assuming that you need the last item for styling.

Option #1 is with pure CSS using the last-of-type selector.

Option #2, is using the get_wp_nav_menu as opposed to wp_nav_menu and once you are inside the foreach, you compare it using count and the current index of said foreach to add the css class dinamically.

Edit: If you are a bit new to WordPress theming, I would definitely go with option number 1 despite not having full browser coverage.