a.Laura Smith is planning for her and her husband Lukes retirement. Both Luke and Laura expect to retire in 35 years (when they turn 65). The life expectancy of men is 75 years and the life expectancy of women is 85 years (i.e., assume that they die the day before their 75^th or 85^th birthday). During retirement (while they are living), the couple wants to withdraw $10,000 at the beginning of each year from their savings account- $5,000 for each of them. Assume that the interest rate during their retirement is 9 percent compounded annually; the interest rate after Luke dies is 10% compounded semi-annually; and, the interest rate prior to retirement is 10 percent compounded annually. How much will they have to deposit in their joint savings account each month (beginning one month from now and ending on their retirement date)?

b.How would your answer change if Luke and Laura Smith expect to inherit $50,000, 5 years from now? Assume that, at that time, they will spend $10,000 for a two-week luxury all-inclusive cruise, spend $25,000 to buy top-of-the-line stainless steel appliances for their kitchen, and save the rest for their retirement. Assume equal monthly payments throughout the 35 years to retirement- i.e., the same monthly payments beginning one month from now and ending on their retirement date.