Bob invested $2,000 in an investment fund on his 21st birthday. The fund pays 7% interest compounded semiannually. Bob is celebrating his 50th birthday today. Bob decides he wants to retire on his 60th birthday and he wants to withdraw $75,000 per year, the first withdrawal on his 60th birthday and the last withdrawal on his 90th birthday. Bob expects to receive $100,000 from his employer on his 55th birthday in recognition of his long service to the company.

Assume Bob has not taken any money out of his investment fund since he initially funded it on his 21st birthday, and that he will deposit the $100,000 from his employer into the investment fund on his 55th birthday. The investment fund will be used to pay for Bob’s retirement.

a) If Bob makes no additional deposits into his investment fund, how much will be available for retirement at age 60?

b) Since the amount in (a) is insufficient to meet his retirement goals, Bob decides to deposit equal annual amounts into the investment fund beginning on his 51st birthday and ending on his 59th birthday, so that he can meet his retirement goals. How much will each deposit be?