Mrs. Chen has saved $22,000 for a down payment and qualifies for a thirty-year mortgage at an annual effective interest rate of 6%. In addition, Mrs. Chen is opening a retirement account that has a 5.2% annual effective interest rate. Mrs. Chen Wants to be able to retire in thirty-eight years, at which point she needs to be able to withdraw $4,100 at the beginning of each month for twenty-five years. Mrs. CHen has $2,600 at the end of each month to use for a combination of mortgage payments and retirement contributions. How expensive a house can she buy? (HINT: Let $M denote Mrs. Chen's monthly mortgage payments. Her contributions to the retirement fund are $2,600-$M at the end of each month during the first thirty years and $2,600 per month each during the next eight years.)