Question 3 (12 marks) (a) Laura Smith is planning for her and her husband Luke's 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 75th or 85th 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 10 percent compounded annually; the interest rate after Luke dies is 12 percent compounded semi-annually; and, the interest rate prior to retirement is 9 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) Now assume that Luke and Laura Smith expect to inherit $40,000, 5 years from now. 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. 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). (4 marks) Question 2 (4 marks) A person joins a pension plan at age 35. How much will s/he have to pay into the pension fund each year in order to accumulate a balance of $250,000 by the time s/he retires (age 65)? Assume that the payments start on his/her 35 birthday and the final payment is on his/her 60th birthday. Interest rates are 7% compounded annually