(similar to) ?(Complex present value?) You would like to have ?$31,000 in 10 years. To accumulate this amount you plan to deposit each year an equal sum in the? bank, which will earn 6 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 ?$31,000 in 10 ?years?

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 6 percent on this? deposit.)

c. At the end of 4 years you will receive ?$12,000 and deposit this in the bank toward your goal of ?$31,000 at the end of 10 years. In addition to this? deposit, how much must you deposit in equal annual deposits to reach your? goal? (Again assume you can earn 6 percent on this? deposit.)