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

a. If you wait one year (January 1 next year) to make a deposit, how much must the deposit be for you to have a balance of $1000 in your account 4 years from today?

b.If you want to make 4 equal payments of each January how large must each of the 4 payments be to accumlate $1,000 if the first payment is made 1 year from today and the last payment is made 4 years from today?

c. If your father were to offer either to make the payments you calculated in part b($221.92) or to give you a lump sum of $750 on January 1 one year from today, which should you choose?

d. If you deposit $750 in your account next January 1, what interest rate, compounded annually, would you have to earn to have necessary $1,000 four years from today?

e. Suppose you can deposit only $186.29 each of the next 4 years(beginning next January 1) but you still need $1,000 when the last $186.29 deposit is made. 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 next January 1. 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%, 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?