Saben is $40$ and wants to retire in $20$ years. His family has a history of living well into their $90$s$.$ Therefore, he would like to plan on living until age $100,$ just in case. He currently needs $$100,000$ and expects that he will need about $80\%$ of that if he were retired. He can earn $9$ percent in his portfolio and expects inflation to be $3$ percent annually. Some years ago, he purchased an annuity that is expected to pay him $$30,000$ per year beginning at age $60.$ It includes an inflation rate cost of living adjustment. In addition, he received $$500,000$ from his uncle BJ when he died. Saben has spent $$200,000$ on his home, but is investing $$300,000$ for his retirement. His Social Security benefit in today$$s dollars is $$20,000.$ Calculate his capital need analysis how much does he need to fund his retirement and how much does he need to save each month to reach that amount?