This is how you define your form tag: <form>
So when submit is clicked, the form calls itself (the page it's on) and refreshes the screen.
You are never processing it, because it never executes "loan-calculator.php"
Even if you executed it by doing this ....
<form action="loan-calculator.php" method="post">
I think it would display the loan calculator but not the other page.
Better yet, JQuery.
If PHP is required to dynamically put numbers into the load "widget",
you'll end-up using AJAX, which is a combination of PHP and JQuery.
Scrap what you're using now and look at some of these: