$(10$ points$)$ Seamore opens an account with no opening deposit. Seamore makes end of quarter deposits over the course of the next $12$ years with the first deposit being three months after when the account was first opened. The quarterly deposits for Seamore are equal to $x.$ Nevermore opens an account with no opening deposit. Nevermore makes deposits continuously at the rate of $20,000$ per year for $12$ years. Both Seamore and Nevermore's accounts earn interest at an annual effective interest rate of $12\%.$ Just after Seamore has made his $48$th and final deposit, Seamore and Nevermore's accounts have the same accumulated values. Find $x.$