Assume that 4 years from now you will need $1,000. Your hank compounds interest at an 8% ansual rate. a. How much must you deposit I year from now to have a balance of $1,000 at Year 4 ? b. If you want to make equal payments at the end of Years 1 through 4 to accumulate the $1,000, how lange 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 will have only $750 at the end of Year I, what interest rate, compounded annually. would you have to earn to have the neecsary $1,000 at Year 4 ? e. Suppose you can deposit only $186.29 each at the end of Years 1 through 4 , but you still need $1,000 at the end of Year 4. What interest rate, with annual compounding, is required to achieve your goul? 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 deposits of equal amounts each 6 months thereafter. If all of this money is deposited in a bank that parys 8%, compounded semiannually, how large must each of the 6 deposits be? Second Part Assume that 1 year from now you plan to deposit $1,000 in a savings account that pays a nominal rate of 8%. a. If the bonk compounds interest annually, how much will you have in your account 4 years from now? b. What would your balance be 4 years from now if the bank used quarterly compounding rather than annual compounding? c. Suppose you deposited the $1,000 in 4 payments of $250 each at the end of Years 1,2,3. and 4. How much would you have in your account at the end of Year 4 , based on 8% annual compounding? d. Suppose you deposited 4 equal payments in your account at the end of Years 1, 2, 3, and 4. Assuming an 8% interest rate, how large would each of your payments have to be for you to obtain the same ending balance as you calculated in part a