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

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

b. If you want to make equal payments at Years 1 through 4, to accumulate the $1,000, how large must each of the 4 payments be?

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 one year from now, which would you choose?

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

e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?

f. To help you reach your $1,000 goal, your father offers to give you $400 one year from now.

You will get a part-time job and make 6 additional payments of equal amounts each 6 months thereafter. If all of this money is deposited in a bank which pays 8 percent, compounded semiannually, how large must each of the 6 payments be?

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