(a) Laura Smith is planning for her and her husband Luke's retirement. Luke and Laura, born on the same date, expect to retire in 30 years (when they both turn 65). The life expectancy of men is 78 years and the life expectancy of women is 87 years (.e., assume that they die the day before their 78th or 87th birthday). While they are living, the couple wants to withdraw $25,000, for each of them, at the beginning of each year (starting on the date of retirement) from their savings account. Assume that the interest rate during their retirement is 12 percent compounded semi-annually, the interest rate after Luke dies is 13 percent compounded annually; and, the interest rate, prior to retirement, is 8 percent compounded annually. How much will they have to deposit in their joint savings account (combine Luke and Laura) each month (beginning one month from now and ending on their retirement date)? (8 marks) (b) Now assume that Luke and Laura Smith expect to inherit $25,000, 5 years from now. If they save the money for their retirement, how much will they have to deposit in their joint savings account (combine Luke and Laura) each month (beginning one month from now and ending on their retirement date)? (4 marks)