You are celebrating your 40th birthday today. You want to start saving for your anticipated retirement at age 65. You want to be able to withdraw $100,000 from your savings account on each birthday for 25 years following your retirement. The first withdrawal will be on your 66th birthday. You intend to invest your money in ABC Bank which offers 10% interest per year. You want to make equal annual payments on each birthday into the ABC Bank for this retirement fund.

a) If you start your first deposit on your 41st birthday and continue making deposits until you reach 65 (i.e. the last deposit will be on your 65th birthday), what amount must you deposit annually so that you will be able to make the desired withdrawals after retirement? Assume that the retirement fund will continue to generate a 10% return per year. (10 points)

b) You expect to receive a lump sum $100,000 distribution from a family trust fund on your 55th birthday, which you will deposit into the ABC Bank retirement fund. In addition, your employer will contribute $1,000 to the ABC Bank retirement fund every year as part of the company's profit-sharing plan. Given this information, what amount must you deposit annually so that you can make the desired withdrawals at retirement? (15 points)