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.
If Bob makes no additional deposits into his investment fund, how much will be available for retirement at age
60?
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?
$170,327 based on the future value of the $2,000 invested for 39 years being $29,267 at age 60 and the future value of
the $100,000 from the employer invested for 5 years of $141,060.
$63,893.50 based on the present value of an annuity due for 31 years, or $994,339 needed for retirement at age 60; this
amount is the future value of a 9-year annuity due, yielding an annual payment of $63,893.50.
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