Getting the permalink by an option from settings api

I am currently using the code from https://alisothegeek.com/2011/01/wordpress-settings-api-tutorial-1/ for my theme’s settings which a have settings where users can input the page slug of an existing page.

My question and problem is, how can i output the permalink of the page slug inputted on those settings?

I tried this,

$termspage = mytheme_option( 'terms_page' );
function get_permalink_by_slug($page_slug, $output = OBJECT, $post_type = 'page' ) {
    global $wpdb;
    $page = $wpdb->get_var( $wpdb->prepare( "SELECT ID FROM $wpdb->posts WHERE post_name = %s AND post_type= %s", $page_slug, $post_type ) );
    return get_permalink($page, $output);
}
echo get_permalink_by_slug($termspage);

I also tried,
echo get_permalink(mytheme_option( 'terms_page' ));

But both of them is not working..

Please help..