(Solving a comprehensive problem) You would like to have $75,000 in 15 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 8 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 the lump-sum deposit be? (Assume you can earn 8 percent on this deposit.)

c. At the end of five years, you will receive $20,000 and deposit it in the bank in an effort to reach your goal of $75,000 at the end of 15 years. In addition to the deposit, how large must your equal annual deposits for all 15 years be to reach your goal? (Again, assume you can earn 8 percent on this deposit.)