?(Complex

present

value?)

You would like to have

?$50 comma 00050,000

in

99

years. To accumulate this amount you plan to deposit each year an equal sum in the? bank, which will earn

88

percent interest compounded annually. Your first payment will be made at the end of the year.

a. How much must you deposit annually to accumulate this? amount?

b. If you decide to make a large? lump-sum deposit today instead of the annual? deposits, how large should this? lump-sum deposit? be? (Assume you can earn

88

percent on this? deposit.)

c. At the end of

66

years you will receive

?$9 comma 0009,000

and deposit this in the bank toward your goal of

?$50 comma 00050,000

at the end of

99

years. In addition to this? deposit, how much must you deposit in equal annual deposits to reach your? goal? (Again assume you can earn

88

percent on this? deposit.)