Vanessa and Joe are the same age. On her 30th birthday Vanessa started to save $2,200 each year for retirement. Joe saved nothing. On her 45th birthday Vanessa will increase her annual savings by 5% a year, each year. Assume all investments will earn a rate of return of 6%. Inflation is 2%.

a) If Joe starts to save on his 50th birthday, how much will he has to save each year to have the same amount at retirement (age 65) as Vanessa? Each of them will save every year including their 65th birthday. (10 marks)

b) How much did each of them save in real dollars? (4 marks)

c) If Joe plan to increase his initial investment by 3% a year every year, how much will he have to save the first year to have the same amount as in part a? (6 marks)