Is Civicrm 4.7.20 compatible with PHP 7.? - only using core components and one extension, cividiscount
If you look at the release notes for CiviCRM you will see various comments about fixes for PHP 7 / 7.1 / 7.2 / 7.3 from around 4.7.14 onwards. Some of those are wide-ranging or critical fixes, others just affect a specific function.  So whether any particular version of Civi works under a specific version of PHP depends to some extent on which bits of Civi you are actually using.

If your site is as simple as it sounds, I'd just crack on with upgrading both Civi &amp; PHP!