Assume that you need $1,000 four years from today. Your bank compounds interest at an 8 percent annual rate.

a. How much must you deposit one year from today to have a balance of $1,000 in your account four years from today?

b. If you want to make equal payments each year, how large must each of the four payments be if the first deposit is made one year from today?

c. If your father were to offer either to make the payments calculated in part (b) ($221.92) or to give you a lump sum of $750 in one year, which would you choose?

d. If you have only $750 in one year, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 four years from today?

e. Suppose you can deposit only $186.29 each for the next four years, beginning in one year, but you still need $1,000 in four years. At what interest rate, with annual compounding, must you invest to achieve your goal?

f. To help you reach your $1,000 goal, your father offers to give you $400 in one year. You will get a part-time job and make six additional payments of equal amounts each six months thereafter. If all of this money is deposited in a bank that pays 8 percent, compounded semiannually, how large must each of the six payments be?

g. What is the effective annual rate being paid by the bank in part (f)?