Mia will retire $10$ years from now and wants to establish a fund today that will pay $$30,000$ cash at the end of each of the first five years after retirement. Specific dates are these: date of a single deposit by Mia, January $1,$ year $1$; date of first cash payment from the fund to Mia, December $31,$ year $11.$ The fund will pay $10\%$ compound interest. How much cash must Mia deposit on January $1,$ year $1,$ to provide the five equal annual year$-$end cash payments from the fund?