Greg Fredericks wishes to have $800,000 in a retirement fund 20 years from now. He can create the retirement fund by making a single lump-sum deposit today.

a. If he can earn 6 percent on his investments, how much must Greg deposit today to create the retirement fund? If he can earn only 4 percent on his investments? Compare and discuss the results of your calculations.

b. If, upon retirement in 20 years, Greg plans to invest the $800,000 in a fund that earns 4 percent, what is the maximum annual withdrawal he can make over the following 15 years?

c. How much would Greg need to have on deposit at retirement to annually withdraw $35,000 over the 15 years if the retirement fund earns 4 percent?

d. To achieve his annual withdrawal goal of $35,000 calculated in part c, how much more than the amount calculated in part a must Greg deposit today in an investment earning 4 percent annual interest?