$(10$ points$)$

A loan in the amount of $800,000$ is repaid with $n$ end of year payments. The annual effective interest rate is $6\%.$ For the first $n-1$ payments, the payment is three times the interest then due. The $n^{th}$ and final payment is the outstanding loan balance due at that time. Find the smallest possible value for $n$ such that the final payment is less than or equal to $25,000.$