There are so many topics on SO about issues with the Ajax.BeginForm not correctly updating the target element with the return partial view:
mvc4 ajax updating same page<
First, install 'Microsoft.JQuery.Unobtrusive.Ajax' from NuGet Manager and later include "~/Scripts/jquery.unobtrusive" in "BundleConfig" after including "jquery-{version}.js"; which will look something similar to this:
bundles.Add(new ScriptBundle("~/bundles/jquery").Include(
"~/Scripts/jquery-{version}.js",
"~/Scripts/jquery.unobtrusive*));